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).