Guide-o-rama: Intro to expressions and equations

This is a Guide-O-Rama reading guide to introduce the basics of "Expressions and Equations" which is its own section of the Common Core Standards for 6th grade Math.
The reading guide begins with introducing some basic vocabulary including expression and more specifically an algebraic expression.  The definition of both of these terms are on page 200 of the textbook.  
The next section goes into detail about parts of algebraic expressions, and defines what a coefficient is.  In order to help students identify that coefficients will not always be super easy to identify (like in the example of 5X, the coefficient will be 5), I had them draw what 5X represents... they should draw an image similar to  
                                X X X X X
With that same reasoning, they could reason that the coefficient for X would be 1 by drawing...
                                                                               X

The next section delves into Order of Operations:
Parentheses
Exponent
Multiplication
Division
Addition
Subtraction 

By prompting students to create their own mnemonic device, they are being creative, and can be silly, and it will most likely be easier for them to remember a mnemonic that they came up with themselves.  Encourage them to share their devices with each other!
    
The "Check Your Understanding" is a way for them to make sure that they comprehend the skills they learned in this section, and they can check their answers in the book as well.  

(Textbook: Everyday Mathematics: The University of Chicago School Mathematics Project       ISBN: 978-0-02-138360-3) 

Building a Community of Learners

     I'm going to step on my "teacher soap box" for this post because this whole chapter is the reason I wanted to go into Education.  The classroom climate is a huge factor in student learning that is so often overlooked.  If a student dreads going to your class, I can almost guarantee they will not listen to your lesson, they will not be engaged in the subject material, and they WILL NOT LEARN what you are trying to teach them.  If a student does not feel safe contributing to classroom discussions, or feel comfortable stepping outside of their comfort zone (which is vital to learning new skills and subject matter) their capacity to learn will be drastically diminished.
     The classroom climate all begins with the teacher-- they 100% are responsible for that.  Teachers who belittle their students, disrespect their students, and do not share the power distribution in the classroom are not creating a classroom that is conducive for creating the ideal "community of learners" that this chapter describes.  The goal of any teacher should be to have their students love their subject as much as they do.  Teachers can do this by being a "champion" for their students (the embedded TEDTalk describes what that is), treating their students as people, not kids that need to be controlled while they are in your classroom, and certainly seen as life long learners.  A successful teacher is one that can spark a students interest in their subject matter.  If I can convince a 7th grader that algebra is cooler than something they saw on Instagram, I would be the happiest teacher ever.

        
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How to Use a Textbook

 

     Unfortunately, when reading this chapter, the thing that stood out to me the most was not the tips on how to use a text effectively, or how to find the balance between coverage and depth, but rather the emphasis placed on teaching for the high stakes tests.  These tests endanger teacher creativity as well as a student's excitement to learn.  If I am teaching a middle school history class, and have a great idea for a fun, interesting lesson about the Boston Tea Party, but also have to cover the entire Revolutionary War in that same week because it is emphasized on the standardized tests what would be the right thing to do?  Do I teach the breadth of information required by Common Core or Georgia State Standards, or teach my students an enriching lesson that might spark a life long interest in history? 
   I went to a school where students were not required to take the State Standards tests (private schools do not have to take the GPS tests), and my teachers rarely used our textbooks beyond teaching subject relevant vocabulary or practice math problems.  A great example would by my 8th grade History teacher, who every year organized a "Second Continental Congress" reenactment for the entire grade; every student was assigned a specific person who attended the Second Continental Congress, and we had to research them, read about them in our book, and come to school on a designated day dressed as that person ready to act, as they did, in the historical signing.  As a future teacher, I often think about my 8th grade history teacher and how he interested me in history; he used our textbook as a reference book, and did not let it replace his job as the TEACHER by simply overloading on reading assignments.
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Think Aloud Reflection

     Initially, I had trouble selecting a "text" for my think aloud presentation.  Between my two subject areas, Math and Social Studies, a historical text would have been the easier, more obvious choice, but because I intend to teach math one day, I found a worksheet that aligned with one of the 7th grade math standards.  This specific standard dealt with proportional reasoning, including interest rates, percentages and ratios.

     While doing my Think aloud, I tried to demonstrate every single step needed to solve the problem, starting with reading the actual word problem.  I am a very visual learner, so when I read a math problem, or anything really, I like to mark up the text by circling things, drawing arrows, and writing little notes besides certain parts.  Once I read the problem through, I went through each step (including the tedious things like long division), and I think I was very thorough in my explanation.

     This process was not as awkward as I initially expected it would be; I did choke at one point when I forgot what 6x8 was.... I can solve calculus and trig problems without a thought, but 6x8 really tripped me up.

     I think when reading math texts, the step-by-step nature of solving problems lends itself better to the think aloud strategy compared to a science text.  Math teachers do have to teach like this all of the time in math; we have to explain each part of he problem because what may be obvious to me probably is not as obvious to a 7th grader. 

For anyone curious if you could pass the a 6th grade math test today... 
https://www.buzzfeed.com/alfredomurillo/math-for-11-year-olds?utm_term=.rbBdDJ9D2#.scELOwYOa

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Synthesis Blog: Teaching finance to middle schoolers

     In my family, we are constantly sharing silly memes, fun articles, or short tidbits about something we heard that day in our family "Listserv" (yes, my family has a listserv... and it's hilarious).  About a week ago my sister, who is getting her masters in Foreign Language Education at Washington University in St. Louis, sent me an article that she claimed I "HAD to read" because it would "change the way I teach math some day."  This article titled "Teaching Middle Grades Math Through Financial Literacy" explores the multiple benefits of incorporating "financial literacy" skills with the middle school math curriculum.  This article directly aligned with chapter 3 of Subjects Matter which addresses the importance of mixing up our students' reading material; adding in things like personal finance articles can do just that!  Students are reading something other than their textbook (which in a math class, is a break that is definitely needed), practicing math skills that follow state standards as well as Common Core standards, and also learning supplementary financial literacy skills that will help them later on in their adult lives. 

    This article suggests including financial literacy skills when teaching topics like percentages, proportional reasoning, compound interest, and even reading/responding to graphics.  The researchers also suggest using the skills of "planning a budget" when teaching basic algebra skills.  Students have to calculate someones paycheck amount based on their hourly wages, how many hours they worked, and then determine, based on the amount of money that they have made, what they can and cannot afford.  Not only are these kind of readings and problems more applicable to real life situations, but they are a small change that any math teacher can make in order to mix up the "diet" of reading we are giving to students.      

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http://www.tandfonline.com/doi/abs/10.1080/00228958.2016.1156526?journalCode=ukdr20

 

Mixing up Reading Material

     Throughout my years in Middle School and High School, especially in my History classes, teachers emphasized the importance of reading primary sources, newspapers and other historical texts IN ADDITION to reading the textbook.  When learning about World War II, we read The Diary of Anne Frank along with the textbook chapters, when learning about colonization, we read primary documents from explorers coming to the American Colonies, and throughout my time in schools, my teachers always had students present "Current Events" projects-- forcing us to read newspapers and scholarly magazines. 
     A key point mentioned in this chapter is the importance of choice for young readers.  You set the boundary of requiring students to be reading something, but allow them the freedom to read about things that interest them; this kind of reading is definitely more appealing than "read pg. 20-56 in your text book for tomorrow." 

(DEAR/Deer joke)

     When I was in elementary school, there would be days where we would walk into history or science class and on the board would be written DEAR... this was my school's version of SSR (pg. 74) which stood for Drop Everything And Read.  It had to be subject related, but we could choose any book we wanted.  Giving some of the power to the students not only allows them to choose reading material that interests them, but it also creates a more even-powered classroom-- a warmer classroom climate.                                                               

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