Text Set Collection 1: Statistics and Probability

Websites

Box-and-Whisker Plot
http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html
Ages: Grade 8 and up
This site gives step-by-step instruction for constructing and interpreting a box-and-whisker plot. It can be used as an exercise to help students make their own box-and-whisker plots or as a quick reference to refresh their minds about box-and-whisker plots.

Central Limit Theorem Applet

http://www.stat.sc.edu/~west/javahtml/CLT.html

Ages: Grade 9 and up
This Applet demonstrates the Central Limit Theorem using simulated dice rolls. The number of dices range from 1-5 and the outcomes of the rolls are recorded in a histogram to demonstrate convergence. I can see this activity being used to quickly demonstrate the theorem and help students visualize convergence under different conditions.

Cliff-Hanger

http://mste.illinois.edu/activity/cliff/#questions%20

Ages: Grade 7 and up

This site contains a fun game that allows the students to visualize probabilities of survival of a "discombobulated" tourist on the edge of the Grand Canyon cliff. It can be used as an interactive exercise when introducing simple probabilities in class.

High School Statistics & Probability Standards
http://insidemathematics.org/index.php/high-school-statistics-and-probability
Ages: Grade 13 and up
This website contains activities for all the Common Core standards covered in Algebra I's Probability and Statistics module. These activities can used or modified by Algebra I teachers to teach the module on probability and statistics.

Let's Make a Deal Applet
http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html
Ages: Grade 10 and up
This Applet was inspired by the a 70s TV show in which the contestants first pick one door out of three doors for a prize (only one door contains the valuable prize). The host then reveals the which one of the two unchosen doors contains no prize and asks the contestant if he/she would like to change the door choice. The Applet shows that there's a higher chance of winning if the contestant switches his/her choice than not switching. I can see this activity being used to intrigue students about using probability to analyze winning/losing scenarios in the real world.

Probability by Surprise

http://www-stat.stanford.edu/~susan/surprise/

Ages: Grade 9 and up

This site is authored by Susan Holmes, a professor at Stanford University. It offers a number of Applets for experimenting and visualizing probabilities and paradoxes. In addition, the site contains class notes for an Introduction to Probability course at Stanford. I like all the different Applets and they can be used to demonstrate probability concepts/phenomenon and capture student interest/attention during instruction.

Probability for Dummies

http://www.dummies.com/how-to/education-languages/math/Probability.html

Ages: Grade 11 and up
The For Dummies web site provides brief introduction of topics such as continuous probability distribution, principles of probability, and discrete probability distribution. It also includes tips for studying probability and a "cheat sheet" for introductory probability concepts. I can see this being used as a resource page for high school students studying algebra and statistics.

Probability Theory
http://www.mathgoodies.com/lessons/toc_vol6.html
Ages: Grade 14 and up
This website contains a virtual lesson on probability. Learners are introduced to probability through simple experiments, exercises, and visual interactivity. Teachers and students can use this site as a resource. Teachers can incorporate some of the exercises and experiments into lessons, while students can explore the page to gain more understanding of probability.

Sampling Distribution
http://onlinestatbook.com/stat_sim/sampling_dist/index.html
Ages: Grade 8 and up
This site contains an Applet for demonstrating different types of sampling distribution and calculates statistical values such as mean, median, standard deviation, variance, and range. It allows you to choose different types of parent population (normal, uniform, skewed, custom) and sample size. I can see this Applet used in introducing sampling data from different parent populations.

Statistics Glossory-Probability
http://www.stats.gla.ac.uk/steps/glossary/probability.html
Ages: Grade 10 and up
This website is organized as a glossory for key probability terms and contains formulas for theorems and rules. Under each term, some examples are included too. I can see this being used as a review resource by college introductory probability/AP statistics students.

                                                   Books

The Cartoon Guide to Statistics
Larry Gonick, Woollcott Smith
Ages: Grade 9 and up

This book portrays statistical concepts in an entertaining manner using cartoon drawings. I can see this being used on a regular basis in a statistics class to explain "dry" concepts in a light and painless way (something to capture students' attention and make statistics more fun).

High School Probability Tutor

The Editors of REA (Author)

Ages: Grade 9 and up

This book contains examples and detailed explanations for problems concerning "probability, discrete distributions, binomial and multinomial distributions, continuous distributions, conditional probability, expectation, joint distribution, function of random variables, and sampling theory." It is a useful resource for students looking for more practices or alternative explanations. It can also be useful for teachers who are looking for supplemental materials and additional practice problems.

How to Lie with Statistics
Darrell Huff, Irving Geis
Ages: Grade 8 and up
This is an interesting read about how statistics (percents, graphs, correlations, trends, etc.) can be used to mislead people. Students can be encouraged to read this book to gain a health sense of skepticism with data and better critical thinking skills.

Statistics Workbook for Dummies
Deborah J. Rumsey
Ages: Grade 9 and up
This workbook contains practice problems and detailed solutions for introductory level statistics (interpreting graphs, normal distribution, confidence level, hypothesis testing, relationship between two variables, etc.). This can be used by both the students (opportunities to learn statistics using another person's explanation) and teachers (see other ways to "painlessly" explain the concepts) of introductory statistics classes.

Teaching Statistics: A Bag of Tricks
Andrew Gelman, Deborah Nolan
Ages: Grade 12 and up
This book contains a set of teaching tips, demonstrations, projects, and examples/topics to make teaching and learning statistics engaging for high school students (and college introductory statistics students). I really like the volume of ideas and teaching tips the book provides for the range of introductory statistics topics. I think beginning statistics teachers would find this very useful when planning engaging lessons.



                       Extra Text Sources (15 and Beyond)

Chances Are: Making Probability and Statistics Fun to Learn and Easy to Teach
Nancy Pfenning

Ages: Grade 13 and up

This book includes probability and statistics activities and explanations for introductory statistics courses. It is likely to be most useful for introductory statistics teachers, but can also be used by any students looking for enrichment or alternative explanations.

Focus in High School Mathematics: Statistics and Probability

National Council of Teachers of Mathematics (Author), Mike Shaughnessy (Author), NCTM (Editor)

Ages: Grade 13 and up

This book contains examples and ideas to teach probability and statistics in high school to better help students develop reasoning and sense making skills. As it is a National Council of Teachers of mathematics (NCTM) book, it is a helpful resource for high school teachers who want to stay current on math educational ideals and research-based teaching practices.

Reflection 8: More On Vocabulary (Baumann & Graves)

My best friend as an ELL.

When I was a new ELL student a little over ten years ago (once an ELL, always an ELL?), my best friend was my pocket translator. Even with my pocket translator, attempting to read an excerpt from the literature book used to take days as I looked up every word's definition in the paragraphs. And even when I knew every word's definition, putting together the meaning was still very difficult due to my lack of understanding for the English syntax. On top of all that, the fact that words often have multiple meanings made reading even more tricky. I remember trying on different definitions until the sentence made sense. Needless to day, reading that literature book was a very frustrating experience. In one of this week's articles ("Commentary: What Is Academic Vocabulary?"), Baumann and Graves talk about teaching "academic vocabulary" starting from the academic vocabulary classifications to selection methods for teaching vocabulary. By dividing the key vocabulary into categories (domain/content-specific academic vocabulary, general academic vocabulary, literary vocabulary, metalanguage, symbols, etc.), teachers can help ELLs and native speakers gain a better understanding of vocabulary and the nature of writings in English.

As the authors said in the beginning of the article, researches on academic language often involve studying ELLs (rather than native speakers). The classification and selection methods for vocabulary teaching in this article would definitely benefit ELLs--especially new ELLs who have little knowledge about the nature of the English language. By bringing to their attention that English academic vocabulary can be roughly divided into a number of categories, what kind of vocabulary words belong to each category, and how does studying words in each category differ, ELLs can gain a better understanding of English as a whole.

"Jerk" in math and physics.

At the end of the article, the authors give an example of different math words in each category (except for literary vocabulary category). Two of the categories that I found important are domain-specific academic vocabulary and general academic vocabulary. Especially in math and science, there are many general academic words that have different meanings than in other subjects and everyday context. Bringing to students' attention these general academic words and how they're unique in mathematical context can deepen students' understanding and even make these words memorable to them. An example is the math/physics word "jerk," which means the third derivative. We had a lot of fun learning about "jerk" in calculus. So, turns out, jerk is the third derivative of the position function, or the change in acceleration (first derivative is velocity and second derivative is acceleration). And when you ride in a car and the car's acceleration changes, you literally feel like you are being jerked around (thus the term "jerk" for third derivative). I think learning about these general academic vocabulary in math could even pretty memorable and fun!

"Jerk" in the real world...

What I like the most about this article (after I looked past how boring it is) is that it suggests to teach vocabulary using academic vocabulary categories. Just knowing what words are content-specific and what are general academic words can help ELLs out a lot when they're "deciphering" the meaning of a sentence. Similarly, native speakers can gain deeper understanding of their language and create and make connections with their existing schema.

Reflection 7: Vocabulary Strategies (Tierney & Readance Chapter 8 and BBR Chapter 5)

Anyone who's tried his/her hand at doing makeup knows that even this art of face

painting requires quite a bit of vocabulary learning.

In Chapter 8 of Reading Strategies and Practices: A compendium  (Tierney & Readance) and Chapter 5 of Content-Area Literacy: Reaching and Teaching the 21st Century Adolescent (Tom Bean, Scott Baldwin, and John Readence), the authors list a number of strategies for teaching vocabulary. Vocabulary learning is a key part in just about any subject and field. As a student, I was never a fan of memorizing words. When given a vocabulary quiz, I would cram them the night before and commit them to long-term memory just long enough to make it through the test. As someone who personally struggles with learning vocabulary and finding the task motivating, I was eager to see what kinds of strategies these reading experts can give.

Constructing a sentence using the vocabulary
word is a part of the personal glossary method.

Four strategies listed in both chapters are possible sentences (first giving students a list of unknown words and known words and asking them to compose sentences, then give students a passage to read, and finally go back to the initial sentences to re-evaluate them), contextual redefinition (use context to guess vocabulary's meaning), feature analysis (use categorization to make distinctions among words), and word map/semantic mapping (using concept maps and hierarchical structure to help students understand vocabulary and concepts). Tierney and Readance give the following strategies: list-group-label (associate terms to topic and then group and label them), vocabulary self-collection strategy (students and teacher both select key vocabulary to be learned, then collect them into a vocabulary list, and extend the word knowledge), and Levin's keyword method (mnemonic strategy in which students come up with a keyword that looks or sounds like the word to be learned). Tom Bean, Scott Baldwin, and John Readence give personal glossary (looking up the definition and compose a sentence to make your own glossary), R^3 (read the word three times and the definition one time), verbal/visual word association (use a 4-box word association diagram), clues and questions (method for reviewing vocabulary by asking students to come up with fill-in-the-blank questions), etymologia (ask students to look into etymologies of words), morphologia (analyzing words based on the morphemes that make up the words).

By giving a bunch of strategies, the two chapters advocate using different methods for teaching vocabulary suited for different purposes/readings/subjects. Vocabulary learning is actually a big part of learning math. Some of the strategies than I can see being used in math include possible sentences (can possibly be used to assess common misconceptions of key terms), word map/semantic mapping (works to organize concepts), personal glossary (ask students to look up the definitions and compose their own glossary--a sure method for all lessons), R^3 (rehearse words a few times might help commit them to memory), verbal/visual word association (4-box method can be used to give non-examples and examples for geometry shapes/definitions), clues/questions (can be used to help students review key terms), etymologia (learning interesting word etymologies can be fun), and morphologia (analyzing morphemes that make up the technical terms to help understanding). As I was writing my math unit plan for another class, I find myself looking for more engaging ways to teach/review vocabulary terms such as frequency, histogram, outlier, interquartile range, and central tendency. An obvious method that's applicable is the personal glossary one. Also morphologia could be used for the word "interquartile." In the unit review part of the lesson plan, clues/questions can be used (students write the fill-in-blank questions for one another to answer). And finally, for particularly important key words, R^3 can be used in class to further help commit their sounds/meanings to long-term memory. However, with an exception to the etymologia method, I wonder how these strategies can be implemented to engage and motivate students (rather than bore them with dry memorization). After all, memorization in learning vocabulary is important, but it can be very dry.

Some "Fun" with Math Vocabulary

Reflection 6: Working with Struggling Readers (D&Z Chapter 11)

Chapter 11 of Subjects Matter: Every Teacher's Guide to Content-Area Reading is on strategies for helping struggling readers. The following six strategies are discussed in the chapter: 1) build supportive relationships; 2) model thoughtful thinking; 3) use activities build engagement with text ; 4) promote self-monitoring; 5) use materials students can successfully read; and 6) provide books and articles on tape.

When you are teaching struggling students,
keep in mind just how much
courage
it takes for them to still be there.

As with struggles in any area in life, it takes a lot of courage to keep trying in the face of repeated failures. Daniels and Zemelman give the following quote by William Glasser to introduce the first key strategy. The psychological concept of compensation takes place when "people who have repeatedly failed at something usually cope by focusing their lives elsewhere to avoid still more failure." As a result, when students struggle with reading or any subject in school, one of the most important thing for teachers to keep in mind is that these students don't need anymore hurt/embarrassment than what they've already experienced from before. Building a supportive relationship with the struggling students--making them feel safe even when they don't succeed and being there to help them--should be a priority. Mathematics is a subject that a lot of people experience difficulty. And because of that, math teachers should make building supportive relationships a priority in their classrooms.

As success is often a powerful ingredient in promoting more successes, choosing materials that the students can read successfully is a wise practice. At times, it might be beneficial to choose text that challenge the students a bit. However, too many challenges in school and life can be simply exhausting. As a result, teachers can incorporate choices in students' reading and vary the reading levels a bit with optional reading assignments. With math, the teachers might consider assigning text reading at or below the students' grade level (might want to choose a text reading below their grade level when they're struggling with math to begin with).

Modeling thoughtful thinking and using activities to build engagement are pretty standard practices that were discussed numerous times in previous readings. Providing reading on tape and making students record readings are strategies to help develop reading fluency. However, I'm not seeing how that is applicable to teaching secondary math.

Teachers want students to become independent
learners.

Promoting self-monitoring, however, is a key practice that students of all levels should have if their goal is to become independent learners/readers. As I wrote in another reflection before, teachers are not going to available throughout their students' lives to teach and assess their understandings. And it's ultimately up to the students to do the work, monitor their understanding, and learn (and eventually, to learn independently). With the increasing emphasis in teacher accountability, teachers are under more pressure than before to be responsible for students' scores and learning. However, as a seasoned student, I can honestly say that teachers (even the best ones I've had) were not responsible for all my learning! In fact, I feel safe to say that my own hard work (and my decision to actually do the work) was responsible for the majority of my past learning. And dare I say that highly motivated students with average intelligence can learn great things with or without a teacher inside the classroom? My point is that all teachers are responsible to keep improving as educators, but the responsibility is not all on them. Perhaps instead of feeling all the pressure of students' achievement, it might be helpful to communicate to the students that they're largely responsible for their own learning.

Reflection 5: Purposeful Reading and "Holding" Thoughts (Tovani Chapters 5-6)

Some reading in life is just...boring.

Chapter 5 of Tovani's book Do I Really Have to Teach Reading argues for giving students a purpose for reading as a way to help inexperienced learners/readers focus on the big picture. Students, who are relatively novel learners in the content area, need something to help them focus on the main concepts--instead of being overwhelmed by all the ideas in the reading. One point Tovani brought up that I think we all can relate to is having to read materials that we find uninspiring. In many cases, not only do we have to read and process those materials, but we also have to come up with something productive to share with our superiors/peers (in Tovani's case, it's being assigned article readings by a former employer). And unfortunately, we cannot simply leave in the fashion depicted in the video below when we encounter unappealing reading assignments (as much as it might be tempting).

Tovani then suggests a productive and less painful way of getting through boring or challenging readings is finding a purpose (purposes such as asking questions, making connections, comparing your own opinions to the author's, or learning about new information) and developing a "conversational voice" with the text (instead of a "reciting voice"). A comprehension constructor (basically a worksheet that helps the students interact and have a conversation with the text) is then suggested for helping students develop the conversational voice with the text. In secondary math classes, the text that students read the most (if at all) is probably the math textbook and the problems in the book. As a math teacher, one could help identify what the student needs to pay attention to when reading a certain type of problem (figure out what information is necessary and what isn't). The teacher could promote a "conversational voice" by modeling her thinking and how she "interacts" with the text/problem.

In Chapter 6, Tovani continues with the importance of "holding" thoughts while reading and suggests a number of strategies for it. Tovani starts off with that we can't simply remember everything we read--especially if the text is challenging. As a result, students should know when and what thought-"holding" strategies to use. A few strategies that are given include using highlighting, sticky notes (to jot down thinking), whole-group thinking, comprehension constructors, double-entry journal/diary, and quad-entry diary. With secondary math, the teachers can use these strategies to help the students make sense of possible textbook reading assignments. In addition, these strategies can also be used to help students organize their learning in class.

Reading is a conversation with the author.

Something that was repeatedly stressed by Tovani is that good readers don't just read a text, they talk to, relate to, and even attack it to make sense of it. Luckily, I have access to a Kindle version of Tovani's book so highlighting and commenting is really easy and sticky-notes/highlighter-free. In the spirit of Tovani's suggestion to interact with the text, I've highlighted the parts in the chapters that I found important, amusing, or that I can personally relate to. One point that I found interesting is Tovani's account of the student Aaron. After re-doing his assignment, Aaron erased his previous mark and wrote "erased" by the erased spot. I found it interesting that Tovani not only went into enough trouble to come up with two possible interpretations (one possible interpretation that Tovani found offensive), but also the trouble of writing this out in his book. It seemed a little odd and doesn't really serve the purpose of this chapter.