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I admit that I am the first to have heart palpitations the moment I hear a problem begin, "A train leaves a station 500 miles east of the city traveling at 60 m.p.h.....".
Yet given time, I am confident I can calculate the answer to a word problem, in part because my early teaching career included two years in a grade 8 pre-algebra class. At that time, I feared my expertise in English/Language Arts was not helpful for covering the math curriculum, so I taught as close to the textbook as anyone can imagine. I depended on worksheets. I was inflexible in my methods. I did exactly what the book suggested I do.
Several weeks into the pre-algebra class, I told a fellow faculty member that I was concerned I could be doing more harm then good. Ms. C had graduate degrees in math, and she was responsible for the more advanced math classes.
"Nonsense," she advised, "just make sure they know their math facts; students who do not know their multiplication tables will never succeed in higher math."
Multiplication tables...I could do that.
"That, and never, ever let them give up." She was firm, "all problems have a solution."
Ms. C was right. I could never let them give up, which meant that I could never give up either. Her prescience about the Common Core State Standards, adopted some 20 years later, is reflected in Mathematic Practice Standard #1:
CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them.
I now understand that this standard should not be not limited to applications in math classes; I believe this standard should be shared with multiple academic disciplines. As evidence, I offer a "retranslation" of this standard's descriptors, explained on the Common Core Website, that I use in every lesson everyday:
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.
If you drop the word "mathematically", this standard measures any student's ability to comprehend a problem, or question, in any subject area, and encourages students to be self-selective on determining the best way to solve a problem. In the English/Language Arts class, this "entry point for a solution" could be anything from selecting an independent book to read, to choosing a thesis for a research paper, or to picking a presentation software for an oral report to name a few examples.
Mathematically proficient students analyze givens, constraints, relationships, and goals.
In the English Language Arts classrooms, I teach students to analyze literary texts, fiction and non-fiction, for givens and constraints crafted by an author; to analyze the relationships between characters or author and audience; and to evaluate the goals these characters or authors achieve or fail to achieve.
Mathematically proficient students monitor and evaluate their progress and change course if necessary.
In the English/Language Arts classrooms, a student often begins writing with one idea or thesis, but by the end of the paper, the idea has changed; the thesis must be re-written. Students must monitor the progression of their ideas, and when the ideas cannot be supported or expressed, then they must change course in their writing.
Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.
In the English Language Arts classroom, students should be able to explain the correspondence created with parts of speech in each sentence construction; they should understand the features and relationships created with punctuation; they should look for patterns in rhetoric; and they should be able to recognize the purpose of a selected genre used to communicate.
Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?”
English Language Arts students must read their writing and the writings of others while keeping in mind the question, "Does this make sense?"For the record, I add the question, "So what?" as well.
The particulars in the MP#1 standard are not limited to mathematics as demonstrated in this almost line by line interpretation. All academic disciplines incorporate the ideas in this standard which, when combined, are the tools of perseverance. Teaching students to persevere is the ultimate goal of MP#1, and there are plenty of opportunities to practice perseverance in the classroom. The incorporation of technology in lessons at any grade level and in any subject can be such an opportunity.
My school has a B.Y.O.D. (Bring Your Own Digital Device) policy for grades 9-12. Our grading system is online, assignments are visible to stakeholders, and almost all of my lessons incorporate some technology during the class period. I have learned first hand, however, that the use of any technology in the classroom requires perseverance because no matter how well a lesson is planned, SOMETHING WILL GO WRONG!
For example: a link on a web page will not work; a platform selected by a student might need Java, which is not available on every device; another student will forget a password; or the network becomes overloaded when 30 students try and access a program at the same time.
I think of the MP#1 when I work on these problems everyday, and I know I am modeling perseverance for my students when I persevere and deal with each problem. I cannot give up and blame technology; I cannot blame the Internet. I must model how to problem solve, how to look for solutions, and show how I regularly ask myself if what I am doing "makes sense."
"Use a different browser," I suggest when a link does not work.
"Let's reset your password," I advise a student.
"OK, Row 3? You will have to wait a minute before trying to log on...we can't all access this site at once," I might recommend.
Sometimes I discover the problem is simply the power supply,"Wait....is this even plugged in?"
Every day, I consider what Ms. C told me years ago as I model the MP#1 standard in my English/Language Arts classroom. From her words to the Common Core Mathematical Practice Standard #1: "Never, ever let them give up. All problems have a solution."