Text Set Collection 2: Relationships and Functions

Ah relationships...can be a uphill struggle in real life and in mathematics.

The final text set is on relationships. Something you can't avoid in real life and in mathematics! Rejoice in the range of book and website selections below! Although they won't be of any help toward relationships in real life (unless you are dealing with a math instructor in distress), may they be of help in learning or teaching mathematical relationships and functions.

Books

Common Core Mathematics, A Story of Functions: Algebra I, Module I: Relationships between Quantities and Reasoning with Equations and Their Graphs

Common Core

Ages: Teacher resource

This paperback published by Common Core's team of math educators and mathematicians includes all the modules in Algebra I curriculum and a sequence of lessons and formative assessments designed to teach each module. As the states are adopting Common Core, I picked this book out because it should be a necessary and useful resource for all teachers trying to adopt Common Core.

From Patterns to Algebra: Lessons for Exploring Linear Relationships
Ruth Beatty and Catherine D. Bruce
Ages: Teacher resource
This book is written by two Canadian educators and is based on the Canadian curriculum. It includes sequenced lessons and ready-to-use lesson plans and activities to teach linear relationships from primary to secondary grades. Even though it's based on the Canadian curriculum, the activities and sequenced lessons could be of great help to all teachers when planning lessons on linear relationships (click the book title above to see a sample of the book).

Authentic Learning Activities in Middle School Mathematics: Patterns, Functions, & Algebra
Brendan Kelly
Ages: Teacher resource
This book contains teaching philosophy and lesson activities for introducing patterns, functions, and algebra. This is a good resource for teachers who are teaching beginning algebra or concepts such as patterns that lead toward beginning algebra.

Growing Patterns: Fibonacci Numbers in Nature
Sarah C. Campbell
Ages: Grade 9 and up (teacher and student resource)
This picture book is on Fibonacci's numbers and their occurrences in nature. Fabonacci's sequence is pretty fascinating and it's a useful pattern to know--both in mathematics and science. When teaching mathematical relationships and patterns, this could be an interesting hook for students.

Websites

Algebra-Class.com
http://www.algebra-class.com/algebra-functions.html#Functions
Ages: Grade 8 and up (student and teacher resource)
This web site contains short lessons on relations, functions, function notation, evaluating functions, linear and quadratic functions, and step and discontinuous functions. Both students and teachers could use this site as a resource. Students can use the content on the site as enrichment while teachers can use the site to prepare or supplement their teaching.

Algebra 1 Online! (Henrico County Public Schools, Virginia)
http://teachers.henrico.k12.va.us/math/hcpsalgebra1/module5-5.html
Ages: Grade 9 and up (student and teacher resource)
This site contains a self-paced unit/lesson on functions, which includes warm-up questions, notes, videos, web resources, homework, journal, and study guides. This could be a useful resource for both eduators and students in teaching the unit on functions and relationships.

Algebra & Functions| Education.com
http://www.education.com/activity/middle-school+high-school/algebra-functions/
Ages: Grade 13 and up (student and teacher resource)
This page on Education.com has classroom activities for algebra & function lessons for middle to high school students. This page can be useful for teachers in search of inquiry-based activities to teach lessons.

Coolmath Algebra.com

http://www.coolmath.com/algebra/Algebra1/#Algebra_1:_Functions

Ages: Grade 6 and up (student and teacher resource)

Coolmath.com has a topic on functions and as you click into each topic, you see selective practice problems and handwritten notes on basic function notation, domain and range, set notation, what is a function, and even the application of functions in the difference quotient equation. These notes can be helpful for teachers when preparing for lessons to see how concepts could be explained by other instructors and for students when they need to see alternative explanations and do a few additional practices (and receive instant feedback).

Functions| Algebra| Khan Academy
https://www.khanacademy.org/math/algebra/algebra-functions

Ages: Grade 8 and up (student and teacher resource)
Khan Academy has a unit on functions and it is broken down into topics in the form of short videos (~10 min.) and example problems. I know that Khan Academy is very well-known, but I still wanted to include this text source as it could be very helpful to beginning educators to see how to explain concepts to students and equally helpful to students who just need alternative explanations (sometimes different explanations just work better in reaching different people, not because they're necessarily superior than the other explanations).

Functions and Relations: Algebra 1: TI Math Nspired
http://education.ti.com/en/timathnspired/us/algebra-1/functions-and-relations
Ages: Grade 11 and up (teacher resource)
This Texas Instrument site provides bell ringers and lessons for the unit on functions. Teachers could make use of the ready-made lesson plans and activities available on the site.

Mathwire.com | Growing Patterns
http://mathwire.com/algebra/growingpatterns.html
Ages: Grade 15 and up (teacher resource)
This web site contains pattern problems and is designed for teaching elementary students beginning algebraic reasoning. Although these tasks are designed for elementary students, high school teachers can use these pattern problems as a lead-in to teaching linear function (or as scaffolding practices).

Mathematics Assessment Resource Service
http://map.mathshell.org/materials/download.php?fileid=1259
Ages: Grade 20 and up (teacher resource)
This lesson plan on "Function and Everyday Situations" is written by University of Nottingham and UC Berkeley. It includes extensive use of formative assessments throughout the lesson to teach how to represent real life scenarios using functions and graphs.

Regents Prep Center Integrated ALGEBRA (Algebra I)
http://www.regentsprep.org/Regents/math/ALGEBRA/math-ALGEBRA.htm#Patterns,_Functions,_and_Relations
Ages: Grade 8 and up (student and teacher resource)

This website is maintained by Oswego City School District and contains lessons, practices, and teacher resources for studying algebra. This website breaks down the subject of algebra into subtopics and under "Algebra Strand," there is a topic of "Patterns, Functions, Relations." After clicking into the subtopics under "Patterns, Functions, Relations," you can obtain a lessons, practices, and teacher resources. This website is good for both the students (site contains lessons explaining key concepts, example problems, and practice problems) and teachers (site contains enriching activity and assignment ideas).

Teaching Functions Using a Lottery: Math Lesson Ideas (Teaching Channel)
https://www.teachingchannel.org/videos/teaching-functions
Ages: Grade 9 and up (teacher resource)
This lesson clip shows a pre-calculus teacher demonstrating an application (lottery car winners) of the concept of function. I like how the teacher engaged the students using the lottery car winner idea and I think an adaption of it can be used to teach function and the 1-1 concept to algebra students.

Journal Article

Smith, M. S., Hillen, A. F., Catania, C. L. (2007). Using pattern tasks to develop mathematical understandings and set classroom norms. Mathematics Teaching in the Middle School, 13(1), 38-44.
Ages: Grade 14 and up (teacher resource)
This article talks about how to use the pattern task to help students develop algebraic reasoning, make connections among symbols, tables, and geometric shapes, and develop classroom norms. It also includes a transcript of student-teacher interchanges inside a middle school classroom. This article was actually a reading suggested by the instructor in my Math Education 482 class and it's my favorite reading from that class. I really like how the author gives a transcript of how she facilitates classroom discussions that empower the students, encourage multiple approaches, and help students develop algebraic and verbal/listening/interpersonal skills.

Let's all get along now.

That's a wrap to the final text set on relationships and functions and my REED 461 Blog! Thank you, my reluctant reader(s)! I hope you all the luck, success, and fulfillment in the world! May we all find happiness in life! And world peace.

Happily signing out,

Xiao

Reflection 10: The Millennial Generation

When I first arrived at Tulane as a college freshman, a four-day long move-in orientation ensued. The most memorable event took place in the auditorium as the college president and deans addressed the entire freshman class all dressed in freshly handed out olive green "Only at Tulane, Only in New Orleans" t-shirts. I remember being told by the deans and president that we "are the smartest class Tulane's ever had" based on our entering class's GPA and SAT scores. Sadly, soon after, that statement was no longer true as each entering class was reported to being more higher achieving (in terms of SAT scores and GPA) than any previous classes. As I read the e-letters sent by my alma mater each spring gushing about its new promising class, I always wondered when my old high school records won't be enough to grant me admission to Tulane anymore (or when will my SAT scores be below the mean SAT score for the incoming class)? Based on that, I always thought of the younger generations as becoming smarter and smarter.

"Class of 2012, I now proclaim you the smartest class at Tulane
--until the class of 2013 arrives!"

One of this week's "reading" is a debate about the Millennial generation. In the debate, Mark Bauerlein argued that the Millennial generation--although having improved behaviors (teen violence, better attitudes toward parents and college, etc.), increased ambition (more AP tests and college enrollment), and enriched resources for intellectual development (increased number of museums and libraries)--is dumber than ever before thanks to the digital age. The digital age, namely social networking and youth's attachment to talking/interacting with peers, makes it hard for adult voices to reach the youth. As a result, young people are reading less (according to self-reported reading hours), their SAT scores are declining, and college professors are reporting that college students are less prepared for college than before. On the other hand, Neil Howe argued that the Millennial generation are not only improving behavior-wise (declining pregnancy rate), they're becoming smarter too. To support his argument, Howe cited the Flynn effect (increasing IQ ages), the fact that there's a vast increase in college enrollment, the positive increase in NAEP Nations Report (especially math), and the comparison of the then and now winning products and words in the National Science Fair and Spelling Bee, respectively.

Skepticism. It doesn't just apply to things
you don't believe or don't want to believe.

First of all, it's very interesting to hear two educated opposite views about how the Millennial generation stacks up to other generations. Especially interesting is how two sides can interpret the same statistics to support their claims. For math teachers, I can see this debate itself (with its statistics) be a hook to teach the power of statistics, how it can be manipulated to support different claims, and how an educated public with a healthy skepticism is needed to not be fooled by politicians and their charts/figures/claims (Do you just believe the numbers that come out of politician's mouth because it's something you want to hear and believe?). For me, the take-away message of this debate is that as educators in the 21st century, instructors (especially the oldies...) should stay current on the culture of the young generations. To do that, he/she can learn about what's it's like to be a teenager nowadays, what's expected of them, what do they value, how much work do they have to do inside and outside of school, and how they communicate and learn inside and outside of school. Teacher expectations/instruction can then be tailored to fit adolescents for maximum learning efficiency/engagement. For example, one of the debate points in the video is the amount of homework and assigned readings (one argues it's decreased and the other argues it's increased). The teacher could simply survey the class to gain an idea of the students' course load and then adjust homework load accordingly. Similarly, how instructors evaluate student work could also be adjusted accordingly as younger generations become more tech-savvy than before. Smartphones, Podcast, and videos are just a few examples of alternative ways to turn in assignments.

Web Resource 2: Math for Dummies

I love how fun and easy to understand the
 For Dummies books are!

As a student, I really love the For Dummies book series. In high school, I've used it to study for ACT, SAT, SAT II, and AP tests and they're usually wonderful in effectively and painlessly explaining concepts and injecting humor into learning, studying, and test-preparation. Heck, I even have access to a New Orleans for Dummies one after having attended college in the Big Easy (awesome city by the way!). In fact, they have books ranging from AP Biology for Dummies to Resume for Dummies to Dating for Dummies (If anyone's interested, leave a comment below and I might be able to hook you up! Hah! I said that as if I have readers.)! I digress. The Math-For Dummies web site gathers the math excerpts from the For Dummies book series. It is organized by topic-by-topic short tutorials and example problem explanations for middle school to high school mathematics students(pre-algebra, algebra, calculus, geometry, trigonometry, probability and statistics, and graphing calculator tutorials). This site can be used by students to quickly review select topics in high school math and possibly decide if a particular For Dummies book is right for them.

In addition to select high school math topics, the For Dummies web site also "Math for Real Life," "Everyday Math for Dummies," and "Technical Math for Dummies." These links explore how math can be used in real life situations. Selective topics include how to estimate taxes when shopping, use body dimensions to estimate length, calculate GPA, quickly calculate tips and perform additions, approach problem solving, and quickly count changes). For teachers, these ideas can help them come up with engaging lesson plans.

This web site is not very interactive: you can click into different links to explore different topics, but that's about it. It is free and does not require any sign up. However, all the excerpts are from the For Dummies book series and the site features the selective books on the right of the screen. So an obvious con is that the purpose of the site is to promote its books by giving readers glimpses of all the excerpts. Alternatively, as a For Dummies fan, a pro is also that you can learn about different For Dummies books to buy to help you with different topics in math. For people not interested in spending money, the site does offer some cool topics and a way to quickly review key math concepts.

Overall, I think this site is best for use outside of class for students (review site) and teachers (resource site for planning) as it doesn't have many activities for in-class instruction. Also, the site features advertisement links on the right that could be inappropriate for school.

Reflection 9: Adolescents' Motivation to Read (Pitcher et al.)

Truthfully, if someone asked me now if I read for pleasure, the phrase "ain't nobody got time for that" and the following catchy remix come to mind.

You see, my definition of pleasure reading usually means reading a long fiction or nonfiction book that's been published. However, when I think about it, I do read blogs/news articles/stories online and engage in email-writing, instant messaging and texting on a daily basis for fun. To me and I suspect a lot of people, Internet reading and communication via writing are integral parts of our lives--like breathing. However, I suspect I'm probably not the only one who doesn't count these activities as "reading."

In a 2007 paper "Assessing Adolescents' Motivation to Read" in the Journal of Adolescent and Adult Literacy, the authors discuss a motivation-to-read study and its implications for teaching adolescents. After surveying 384 adolescents and interviewing 100 of them in grades 6-12 in the United States and Trinidad, unsurprisingly, the authors found a discrepancy between survey and interview results. The interview results suggest that many teens actually do a lot of reading for fun outside of class even though they identify themselves as ones who do not read for fun. This discrepancy suggests many adolescents have come to define reading as strictly academic reading (reading done in school) even though many of them do enjoy "reading" outside of school in the form of reading magazines, emails, stories online and written by friends, and exchanged on IMs. At the end, the authors give the following five suggestions to teachers of adolescents: 1) incorporate the multiple literacies students read outside of school into instruction; 2) model reading enjoyment; 3) use activities such as literature circles and book clubs to engage adolescents; 4) vary reading difficulty levels in reading assignments;  5) and involve student choice in reading.

Incorporating student interests into teaching is a
sure way make most (if not all) topics more engaging.

The paper, using motivation scores and interview data, quantitatively and qualitatively sums up the fact that students tend to find reading in school different and less fun than reading outside of school. In addition, students tend to reflect on their reading abilities based on how they do in school-related reading tasks that emphasize "decoding skills and comprehension strategies" above "positive attitudes" that "are essential for mastery of a text" (395). The authors suggest that teachers should incorporate student interests into teaching and promoting reading skills. Inside a high school math class, the teachers can involve adolescent interests (cars, fashion, food, people) into tasks/problems. Once you have the students hooked, teaching how to read and identify key facts in math tasks/problems and how to use math concepts could proceed more smoothly and painlessly. Also instead of relying on textbooks, some bold math teachers can even use Internet or outside sources to find other more engaging problems and readings to teach their lesson with. Luckily, for math teachers, teaching math and associated math reading probably don't entail over-analyzing every little detail for meaning that so often takes the fun out of school-related readings (Yes, I'm looking at you, English teachers. Love you all. And you were my favorite teachers in high school, but sometimes I can't stand the over-analyzing).

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