Text Set #1: Probability and Statistics

Books

• The Cartoon Guide to Statistics

Larry Gonick and Woollcott Smith (authors

Grade Level: 9 and up

This book makes statistics fun for anyone! The authors have created several situations that use play-on words to create comical stories that accurately present the material. This book could possibly replace the textbook.

• Focus in High School Mathematics: Reasoning and Sense Making in Statistics and Probability

J. Michael Shaughnessy, Beth Chance, and Henry Kranendonk (authors)

Grade Level: 9-12

NCTM published a series of books that help students focus on reasoning and sense making in various subjects. This particular text focuses on six investigations that show students how the skills they have learned in class can be applied to a real problem they might encounter themselves. It is a great resource for teacher to use in class with their students!

• Why Do Buses Come in Threes?: The Hidden Mathematics of Everyday Life

Rob Eastaway and Jeremy Wyndham (authors)

Grade Level: 9+

Students need to see math in real life in order to fully appreciate it for what it is worth. This book poses several questions and analyzes them mathematically to show its readers how people can use math as a tool to solve real problems. This is a great read for high school students and teachers alike!

Websites

• Probability

http://www.mathsisfun.com/data/probability.html

Grade Level: 7+

This site is great for showing complex topics in a very simplistic way. My favorite part of this particular page is the probability line because it shows a visual representation for the range of possible probabilities. The site also gives some practice problems that are multiple choice, and the solutions are provided!

• Gapminder

http://www.gapminder.org/

Grade Level: 9+

Teachers cringe when students always ask when they will use math in the real world. Well this site is great for these students! Gapminder shows interactive data that can be played over a timeline. For example, students can watch how CO2 emissions have increased in each country across the globe over the past 180 years.

• Statistics Online Computational Resource

http://www.socr.ucla.edu/SOCR.html

Grade Level: 9+

Students are comfortable working on computers in today's time, so having online resources can really engage the class as a whole. This site presents students with virtual experiments, games, and distributions that help students learn more about statistics in a fun, interactive setting.

• Math Goodies

http://www.mathgoodies.com/lessons/vol6/intro_probability.html

Grade Level: 7+

When students are confused about the difference between an experiment and an outcome, they can go to this site to help them refine these skills and test their knowledge. The site is visually appealing and includes a spinner and die that students can actually spin or roll to test what should be expected. There are even five questions at the end that can give immediate feedback.

• Braingle

http://www.braingle.com/Probability.html

Grade Level: 9+

This site is a great resource for students to use to practice applying probability to solve riddles. It provides a hint and answer for each riddle, so the students can choose how much they want to see before seeing the solution. These problems teach students to read carefully and analytically. Each riddle has a ranking for the level of fun and difficulty. It is a great resource for students to practice on their own!

Articles

• Fantasy Baseball with a Statistical Twist

Lori Koban and Erin McNelis (authors)

Grade Level: For teachers

This article shows teachers a great way to incorporate statistics in a project that is relatable to the students. The project has students analyze several different important traits of baseball players, and they must use this to inform their decision for their fantasy team. The article gives an excellent description of each step of the project, and the students should have a lot of fun doing these types of analyses.

• Rare and Exotic Probability Bugs

James R. Kennis (author)

Grade Level: For teachers

Students often arrive at the correct answer when calculating probabilities, although they may arrive at this answer using incorrect processes. This article analyzes a few of the most common mistakes that students can make in the thinking process, which teachers can anticipate when they are teaching basic probability concepts.

• Shooting Free Throws, Probability, and the Golden Ratio

Terry Goodman (author)

Grade Level: For teachers

Many people love watching and/or playing basketball, and students can use basic probabilities to analyze their free-throwing skills. The article shows many different approaches to presenting the data. For example, a Punnett square is used to show the probability of making both free throws, making the first and missing the second, and finally missing the first which means the second free throw does not matter. Functions are then created and graphed to show the probability of making a free throw given a certain percentage for each player. This is a fun way to get students to look at situations analytically to make improvements in the future!

• Analyzing Highway Speeding Data in the Statistics Classroom

Paul Laumakis (author)

Grade Level: For teachers

By the time students are taking a statistics course in high school, they are likely old enough to drive. Using a topic like this is a great way to show students how statistics can be applied in real life. The article looks at highway speeding data at two locations, and students should see the patterns that occur at both of these locations. They can then make decisions about how they should drive while they are at these locations, and they could even take this data to the police if necessary to show them how fast some people are driving through these areas. Statistics teachers should really consider giving this project for students to complete, not just for the practice of comparing two data sets.

Online Articles

• Stories vs. Statistics

John Allen Paulos (author)

http://opinionator.blogs.nytimes.com/2010/10/24/stories-vs-statistics/

Grade Level: 12+

This article shows the difference between posing hypothetical situations and analyzing real-life events. This highlights the fact that probabilities rare merely what you should expect out of a certain situation, not what is certain to happen. The author uses examples with which everyone should be familiar to show the relevance of statistics and probability. It is a good read for enriching those students in a statistics class.

• Probability of Playing College and Professional Baseball

http://www.hsbaseballweb.com/probability.htm

Grade Level: 9+

Many athletes have a dream of playing professionally and living a generous lifestyle. I am not saying that teachers need to crush their students' dreams, but I think that students need to know the reality of the dream for which they are reaching. This site gives a table of values from the NCAA with statistics about high school, college, and professional athletes. Students could possibly use sites like these to see where probabilities are found in their lives.

• Did You Know: High School Facts & Figures

http://www.stageoflife.com/StageHighSchool/OtherResources?Statistics_on_High_School_Students_and_Teenagers.aspx

Grade Level: 9+

Students often see statistics as a challenging subject that uses numbers as words. However, statistics give meaning to situations in real life, and this article helps students see how they compare to other teens in many different areas. This site shows how much students watch television, how students watch/read the news, how students spend their summers, and many more universal topics like these.

How to Teach Vocabulary to Students

The Bromley article for this week was a light read that was full of practical information for teaching new words to students. Math can be a difficult subject to learn and teach because students have to first understand what is being asked of them, a task that can be made easier if the teacher has the ability to effectively teach vocabulary. 

One of the first things I took from the article is that "English is three times larger in total number of words than German and six times larger than French." Many of the words are derived from other languages, and we tend to combine and fabricate new words daily. Despite the large size of the English vocabulary, I was shocked to read about how much simpler the English language is compared to other languages. Although there are several exceptions for word pronunciations, many English words can be phonetically broken down and spoken accurately.

However, one of the worst aspects of the English language in my opinion is the fact that words can have so many different meanings depending on the context in which the words are used. Product is a perfect example of this. In math this term is the result from multiplying two quantities together, but it might not have this specific definition when used in another context. Math is full of words that mean something very specific, and I think many students struggle to see the importance of using proper vocabulary when speaking and writing mathematically.

My favorite statement from this article: "It is more effective to teach fewer words well rather than several words less well." I just felt like this sums up everything that we have discussed in this article and in this class, as well. The whole purpose of teaching vocabulary is to increase reading comprehension, and this brings a whole new meaning to the phrase "less is more."

Building Strong Vocabularies

One of this week's readings talked about how to develop vocabularies in the classroom, a concept that I'm sure is important throughout any content. When I see a student who is frustrated in a math class, I try to ask them what exactly it is that is making them feel uncomfortable. The most common answer is, "I just don't understand what you are even saying!" This shows just how important it is for students to be able to talk the talk. I must do something as a teacher to help my students develop the proper vocabulary if they are to succeed in math.

The first strategy listed in chapter, Personal Glossary, is one that I fully intend on using in my classroom. I remember when I took geometry in high school, we had to keep spiral-bound index cards filled with definitions, theorems, and postulates. We were constantly being quizzed over vocabulary words! Once we had a firm grasp of these words, the problems suddenly became much easier to work when we could apply these theorems and postulates to solve problems.

Another strategy that could be used in conjunction with the Personal Glossary is the Verbal and Visual Word Association. This strategy reminds me a lot of the Frayer model. Students write the word, an example, a non-example, the definition, and possibly a picture to help them remember the word. This would be a great way to organize each individual word, and then the students can have all of these association arranged in their personal glossary.

Vocabulary is such a crucial piece of the learning puzzle, but I think focusing on developing vocabulary is an easy way to build confidence in students. Once they feel comfortable with vocabulary, they will hopefully feel more confident when approaching math problems.

Strategies for Developing Critical Reading

I enjoyed reading this chapter because I felt like I learned effective ways to get students to be critical of what they read. I really like the Polar Opposite strategy because there is no right or wrong answer, but students must support their reasoning behind their choice. However, I do not really see how this could be easily incorporated into a math class. Maybe I could have my students look at a student's work and have a Polar Opposite where "algebraically" and "geometrically" were my words. They would have to place where the student's approach lies on this range. 

Opinion-proofs are great for developing students' skills in showing support for their opinions. Again, there are no right or wrong answers if something is a true opinion. The reasoning fallacies on page 161 should be stressed when having students defend their answers, and I may even print them out and post them for the students to constantly see. There are multiple pathways that can be used to reach the correct answer in math, so having opinion-proofs can get students thinking about what the "best" way is to solve a problem. Other people may think better algebraically than numerically, but they should defend their reasoning when explaining their answer.

The Phony Document strategy reminds me of the Centaur display in the library on campus. I think math problems could be easily set up in a phony document, and students would have to read critically for the mistake in the reasoning shown. For example, all of the math interns have seen the famous "1=0" problem that "proves" that 1 is equal to 0. However, there is a flaw in the math that many people overlook. This strategy lends itself best to math, in my opinion, because students have to really read analytically in order to identify the flaw.

Tovani Chapters 5 and 6

I find myself relating so closely with the stories presented throughout chapter five. Sometimes it is quite difficult for me to think about how someone would think about a topic for the first time. For example, I had to teach the laws of exponents to my students two weeks ago, and it was a challenge to know how to explain this to them. I feel like this is a very elementary topic, but I have also been using these laws for many years now. The instructional focus guide sheet could help me determine what the main focus should be in assigning reading on topics in math. Not only should I be focusing on the main ideas of each topic, but I should also teach the students how to turn off their reciting voice and turn on their conversation voice. Reading a math textbook can be difficult because the text is so dense. I want to encourage my students to ask questions and work out the sample problems with the text so that they are really conversing with the author. Then, they can ask questions in class that help clarify and deepen their understanding of the material.

Chapter six gives several tools to help students hold their thinking to remember and reuse. I think it may be worth the time to show students how to mark up their textbook with sticky notes because they may seem overwhelmed at first when they are reading to learn the material. However, my favorite strategy in this chapter is show on page 82, the Quad-Entry Diary. I can see myself using this with many different topics in math. This seems to be a great way to get students to write things down on paper in an organized manner to help them remember what they have read about and/or discussed in class.