Using literacy in the math classroom...

Where this is a final assignment of sorts, I am going to address it a little differently.  For starter, kudos to Amy Wilson and Allen Smithee for making this post so easy!  What I mean by this is that every one of these questions are something that we should have already addressed.  If they haven't actually been discussed in an assignment, I know they are all things I have given some serious thought and consideration to in this class!  So, with that in mind, here goes...

(I will be addressing these questions in relation to my math discipline)

- How will you choose and teach vocabulary words?

Part of me really wants to be sarcastic right here and say that I will help my students learn new words and terminology!  While that is true ;), there is a definite process to doing this.  I have spent a lot of time in SCED and methods classes learning about scaffolding.  The way I see setting up scaffolding for my classes is this:  If the scaffolding has a good solid base it can safely reach much higher!  This is how I see vocabulary- it is the most important part when it comes to the base of the scaffolding.  It is going to take time and work, but there are words and terms that my students will need to know, be comfortable with, and be able to actually use before they can actually understand higher thinking concepts in math.  Not only is this important in my class, but these words will be used throughout their math career.

So, how are the words chosen?  At the beginning of every new unit I plan to introduce any new or troublesome vocabulary at the onset of my lessons.  By new or troublesome, I mean terms that are both new to the student and term that may not be new but that have a different meaning in math than they do in other disciplines.  I have discussed vocabulary in other posts so I won't drag this on, but it is important for the students to learn the word, write it and the definition to become familiar with it, see it used as an example (many of these words/terms are actually math concepts and processes), and be comfortable with it in the context of a math problem/assignment.  It isn't enough to introduce the word and then move on.  It needs to become a part of the language of my classroom.

- How will you support your students in writing texts and producing other representations in your discipline?

This is something that I actually focused on in my text set, oddly enough.  This may seem like an odd addition to a text set list, but it’s one that will be a must in my classroom.  There is something to be said for journaling in a math class!  I fully plan to have a day every 2-3 weeks where we participate, as a class, in a lab/project and do all of our written work in a journal.  These will be projects that include a central problem solving question, will provide opportunities to graph, work through mathematical statements and equations, utilize charts and/or tables, and take detailed notes on all of it.  The purpose is 2 fold.  Not only does this provide excellent notes, but it also provides a sense of pride and completion.  There is something to be said for looking over a year of entries and realizing what you have learned!

While this is just one example of my students producing their own texts in my classroom I think it is one of the most important.  Another is the use of GeoGebra to create visual representations of what they have learned.  GeoGebra is something that I refer to in an earlier blog post.

- How will you support academically, linguistically, and culturally diverse learners?

Now this is something that every teacher needs to address.  The truth is that this is one area that frightens me more than most, but also one that I really look forward to learning more about.

I have this huge advantage in my math classes that I don't exactly have with my ELA classes.  Math is a universal language!  That being said, math problems and text books aren't exactly universal in nature.  One big thing that I have learned when working with culturally diverse students is the use of peers.  I live in an area with a large hispanic population.  Students are always ready and eager to translate for each other.  The goal here is to make sure that they are having to translate less and less as the year goes on.  Also, as we learned in class this semester, gesturing, visual representations, repetition, and continued practice go a long way in helping students from all backgrounds understand. 

The other thing to remember in this situation is that learning goes both ways.  I have as much or more to learn from my students as my students have to learn form me, and this is also the case with diverse learners!  Also, when it comes to academically diverse students schools are equipped with wonderful Special Education programs that provide IEPs and 504 plans are also available to those students who meet different requirements than those offered by special ed.  These programs provide not just guidelines for teaching these students, but resources in the way of classroom aides and added individualized instruction.  Having been an aide myself I know how wonderful these resources can be when departments work together for the benefit of the student.

- What kinds of texts will you make available to your students? 

Hopefully I don't seem like I'm taking the easy way out on this one, but I am very proud of the text set I completed this week.  I think this is an excellent place to share that for some person that may find this blog in the future as well as my future students and their parents.  I have a text set list that I am going to provide as a link titled "Math Text Set" and found on the right side of this page.  Feel free to browse it and you will notice that I plan on using and having available a wide set of text for my students.  This list is just the beginning.  I am hoping this list will continue growing at a rapid rate as I continue to find more items to add to it and as the math world continues to change!

BOOKCLUB!!!

What a great new experience for me!  I have never been in a book club.  To be honest, I have never really wanted to.  This changed my mind, a little bit.  While I am not at a point right now where I have the time for being in a book club, it is something that I want very much to introduce into my classroom... But let's start with my experience.

Kristy Bradshaw and I decided to read 2 books, Slaughterhouse 5 by Kurt Vonnegut and Dark Life (Book 1) by Kat Falls.  Can we say opposite?!  These books were so different, but I have to say that something unexpected happened.  I thought I would like my book more, but I fell in love with Kristy's.  I chose Slaughterhouse 5.  This was a very different book that put a spotlight on what happens to our troops.  While we don't want to consider that people may deal with this type of trauma by completely losing in, that is what Billy Pilgrim, the main character in the book, actually did.  This book can also be taken in other ways.  While I saw it as a story of a man ravaged by the effects of war, Kristy saw it as a science-fiction story.  It's amazing all of the different perspectives you can come up with when reading a book.  This book is definitely one that is most suitable for 11th and 12th grade students.  It is actually on the 12th grade core reading list.  That is one of the reasons I chose to read the book.  I have not been quick to dive into the required reading list, but found quickly as I got into this book that there was no reason to be apprehensive.  These are great books!  While I may not be a fan of all of them, I can for sure see why they are required reading.

Dark Life, on the other hand, is not just a science-fiction/fantasy book, and Kat Fall's first!  It is hard to believe that this is her first novel.  The lady really knows how to appeal to middle and high school students.  Not only that, but I loved the book as well.  I have always thought that I am not a sci-fi and fantasy girl.  I love John Grisham, plain and simple, and tend to venture out of that realm only when a book is recommended, relates to the mystery/law type platform, or is required reading.  That doesn't mean that all I read is John Grisham, but sic-fi is the one area that I have actively avoided.  That being said, there are a lot of sic-fi movies that I love!  The funny thing is that I have read a few sic-fi/fantasy books lately and have thoroughly enjoyed them all!

Back to our "book club."  We did something a little different.  Because I am in Holden and Kristy is in Beaver, we held our discussion on a google doc.  While I am hoping Kristy doesn't kill me, I feel like the best way to share our discussion is to actually share the doc.  I will provide a link at the end of my post.

Before I wrap this up I would like to discuss what I felt was the biggest thing I gained from this project.  I will hold book clubs in my classroom!  This is something we talk about in the google doc, and here is what I came up with:

I think I might look into having some small reading groups where 3-5 kids form a reading group (maybe according to reading ability levels- I’ll have to work that out later), and they pick a book that they will all read during the first 8 weeks of each term.  Every 2 weeks we could hold a group discussing in class where the group gets to discuss the ¼ of the book that should be read by that point.  Then in the last 2 weeks of the term I could give them a day to make an ad poster about their book that would make the rest of the class want to read that book.  Depending on school policy I think it would be awesome to hang these posters in the hall by the library.  I have never been in a book club or reading group, but I think it would be a good way to help some students enjoy reading more.

This is the read only link to our google doc.  If you want to take the time to actually read through our discussion, you will find that we are a lot like our students.  We comment on how crazy the author must be, mostly in relation to Kurt Vonnegut, and express what we really did and didn't like about the books.  While you may not want to read through the doc, I think it was a really handy and interesting way to hold a "distance book group."

https://docs.google.com/document/d/1cqIehnC-lRjn-uF9270fRK2HMrrI5-BocYiGZE0kKfg/edit?usp=sharing

The Annual BYU Bridge Building Contest

Authentic Question:  Is bridge building more about the materials or the design?

When this is asked to a classroom loaded with math/physics nerds it isn't just a question, it's a challenge.  As such, it was one of the most memorable teaching moments in my high school education!

Our answer- we can build an awesome bridge out of whatever you give us!!!  We're just that amazing.

Uptake:  All right, so if I had you build a bridge out of balsa wood, you could make it strong enough for me to stand on?

Our answer- of course!  Where's our truck load of balsa wood?  Nope, not that lucky.  We each got a little kit to build a small bridge that would be put through the ringer!  We had some balsa wood sticks that looked like wimpy shishkabab skewers, glue, little wood blocks to go at the pressure points, and a strip of cardboard.  We were told one beam of the bridge would have to hold more weight than the others and then we were let loose with all of the math and physics knowledge that our little brains could muster!!!

Some of us had brilliant dads that insisted we had to use an I-beam design.  Mine also insisted that I use every last drop of glue even if it was just to coat my I-beams and theoretically make they stronger (in a world free of torsion!)

Level of Evaluation:  Now I'm pretty sure this step was used to get into our heads!  Our teachers would say things like, "That's a good idea, but have you thought about directional force when it comes to that beam construction?"  Or, "I like that... as a good jumping off point."  What!?  It took me 4 days to get to what they called a jumping off point?!

Cognitive Level:  I have to say that my 16 year old brain had never operated at such a high cognitive level, and my teachers, knowing what I was capable of, made sure to push me to my limits and a little bit beyond.  I can honestly say that no matter the learning level of the student in the class every one of us felt challenged.

Finally we began bringing bridges, and most of them looked something like this...

There were variations of course, but you get the general idea.  Then some Senior Engineering student from BYU with a sick sense of humor put them in this machine to make our faces do this...

And inevitably this happened...

As soon as your bridge broke the machine would stop applying pressure.  The pressure of each piston was taken and added together to come up with a combined pressure for your bridge.  I never cracked 500 lbs.  That's right, my little balsa wood bridge held a combined weight of just less than 500 lbs.  The current record rests somewhere around 2400 lbs!  Which brings us to the final element of a great lesson...

Question Source:  Well, that would totally depend on the question, wouldn't it?  Was it:  How much weight can a balsa wood bridge hold?  How would you construct the best bridge?  What would happen if I added a brace here?  What will happen when this beam begins to twist?  or How can I build a better bridge next year?

These questions came from all of us- teachers, students... even administrators and parents!  No wonder I remember building my bridge and the lessons it taught me.  It wasn't your everyday classroom lesson.  It was teamwork, competition, and problem solving at its finest!

How Can Critical Literacy Help Me?

When we think of the word "critical" what first comes to mind?  It could be that someone is critically injured and might die, that a piece of information is critical and therefore very important... It could refer to a lot of things, but let's really think about Critical Literacy and how it can help each of us.


All of the words in the image tell us something about critical literacy.  This is a process that helps us all look closely at something, understand it, and use that understanding to gain meaning and knowledge that will lead to change!

Let's use critical literacy to think about math!  Who is good at math?... Let's see... Einstein... Newton... Leibniz...

So basically a bunch of kinda funny looking dead white guys...

Well, they might be pretty awesome, but I don't think they're the only people that are good at math.  I happen to believe that WOMEN are pretty good at math, too!  And you know what else, it's not just white people who are good at math.

I had a teacher that, even though she was a female math teacher from 1965-1995, believed with all her heart that white boys would succeed more in her 7th grade math class than anyone else!  Let's CRITICALLY look at the area of math to find out what's wrong with this picture.

What is one of the biggest barriers to anyone in education!?  Honestly, it's reading.  If we get down to the basics we will find that if you can't read then it's really hard to learn.  Who tends to struggle the most with reading in our American schools?  I would have to say it's those who grow up in homes where English isn't the primary language that is spoken in the home.  You know what the great thing about math is?  It's a universal language!  As long as we can understand each other and understand the problem that needs to be solved, then we can do the math!!!

I had one of the best students 3 years ago.  I knew he was smart, and he was really good at math.  There was only one problem- he was in 8th grade and read at a 1st grade level.  So guess what, did we work on math to get his math grade up?  Nope- I read him his math problems which he then did perfectly, and we worked on reading!  Turns out that his teachers started figuring out that he's pretty smart.  Is he white?  Nope.  Is English the primary language spoken in his home?  Nope.  Can he find the area of any three dimensional shape?  You bet he can!  But do you know what he likes to do more than that?  Solve problems that deal with money.  And do you know what his non-white, non-english-as-a-first-language-speaking female cousin likes to do with math?  She likes to figure out speed and acceleration.  She loves physics!  Do I want a classroom with all types of students who love all types of math?!  YES!!!!  I really do!!!!

There is a way to change what we believe about math- to challenge what it always has been.  It involves people.  It's about their interests, their abilities, and their individual success.  Math is very rarely the problem- the problem is trying to bring the student to math and not the math to the student.

Digital Text in the Classroom

One of my first introductions to Digital Text when it relates to math was in Math 3310 at USU.  We used the program GeoGebra.  I love that program and would like to use it in my classroom!  Now after some reading on digital text and it's importance, help, and much needed place in the classroom I plan to use it and many other digital platforms.

My new favorite is Desmos.com.  I just spent the last hour playing with my own graph!  I would love to spend some time drawing faces and other images with this program.  I think Desmos provides students with a great opportunity to use their own imaginations and their math skills to create fun images.  I have seen and read about the importance of expression and change for students.  Not everyone is made to sit in a desk and read a book- and that's a very good thing!  I would like to challenge my students and allow them the opportunity to do fun new things in the classroom by using digital text.

Here is an example of what I did today...

https://www.desmos.com/calculator/inrlvp0xvt

When Professor "PAIN" Made Me Work...

Before I start my story, I chose to focus on my English discipline this time.  I believe in the value of math writings and found the reading/powerpoint on that topic to be insightful and incredibly helpful!  However, I had a very specific incident in my life that led me to my English discipline, and as you read I'm sure you'll see why...

I was one of those students.  I knew how to play the system.  I started out as one of those bright-eyed, eager-to-learn, brown-nosers, and morphed into what I would later realize was, well, lazy!  Now, before you think I'm trying to boast, realize that I am very aware that what I needed was a work ethic, and possibly a good kick in the pants!  I had the brains, I just didn't see the reason to work hard.  I worked hard and did what a good little nerd was supposed to all the way through 8th grade, and then I started to figure it out.  Almost all of my teachers gave some type of extra credit on tests.  Tests were not a problem for me.  Class work was often dull, but I could do it in class.  What I really didn't like was homework.  Not because it was hard, just because I didn't feel like doing it.  I learned beginning in 9th grade that it didn't matter if you had 96% or 106%, the grade was still an A.  And with my extra credit I would do just exactly enough to get the 96%.  In 10th grade I "stood on principal" in my Honors World History class and refused to do any work through most of the first term because I found it "morally objectionable."  I don't remember what offended my delicate sensibilities, I just remembered that was the first and last C that I ever brought home- it did not go over well!  After that, however, I decided an A- was still an A, and slowly became perfectly comfortable with an occasional B+.  Those are fantastic grades, but I was capable of more.

Yep, I became lazy.  Unless the teacher demanded more out of me I did just enough to still bring home that 3.75 that my parents required in order for me to keep driving.  Luckily the "C Term" as it became known at my house came around before I started driving!  Keep in mind, I had teachers I worked for.  My AP American History teacher, Mr. Knight, was so passionate about what he taught and had such charisma (yes, we actually told him on a regular basis that he, in fact, had charisma) that it was hard not to get caught up in the tale of Women's Suffrage and the Industrial Revolution.  That man deserves a lot of credit for teaching me how to write a DBQ (Document Based Question) essay for my AP Exam.  I actually quite enjoyed all of my AP classes.  Looking back now I realize that it was because those were my quality teachers who really knew how to engage and challenge me.  

Like I said, I wasn't dumb.  With AP and Concurrent Enrollment hours on my side, I enrolled at Dixie College in 1998.  Because I already had 38 credit hours I graduated the next spring.  But Dixie is where the "Pain" began...

Meet my best friend through part of high school and my year at Dixie- yep, it's a baseball.  No, I didn't play for Dixie.  I played with this little guy under my desk.  Most of my family suffers from what my baby brother calls ADOS... Attention Deficit, OOH SHINEY!!!  Needless to say, if our hands aren't busy we aren't paying attention.  I met Professor Allen Payne the first day of my Spring semester.  He was my English 2010 professor.  English 2010 is all about writing, and guess what, I can write.  No need to worry, right?  

...And then I dropped my baseball.  First day- I dropped it, which never happened until that day- it rolled to the front of the classroom and hit Professor Payne right in the foot.  Now, one of Payne's arms was paralyzed from a stroke, so he had to reach across himself, maintain his balance, and pick up the baseball that one of his very new and very rude students just had the nerve to drop in his class.  He informed me with a stern veteran teacher tone that I could "have it back at the end of the year."  Ten minutes later he gave it back with implicit instructions to hold still and pay attention.  And that was it... I was on his radar.

I wrote 2 seemingly impeccable essays and received a B on each.  I couldn't understand!  I met the criteria, I covered the topic, and I stuck to the format guidelines.  My MLA was perfect... what more could he want?!  It was at that point that he asked me to come to his office and meet with him during my hour break between classes.  

You see- he had researched me.  He looked through my high school transcripts, my SAT and ACT scores, the classes I had taken and the grades I had received.  And he figured me out.  He informed me that I was going to earn every ounce of whatever grade I earned in his class.  He wanted to meet with me regularly and he wanted evidence that I was working my little 19 year old butt off!  He was offering help and variety when it came to writing opportunities, and he wanted quality and variety back.  We were already laying the groundwork for our big research paper for the semester and he wanted to be involved in the entire process.

I wanted to write something about Judaism- I was fascinated by the Jewish culture and really wanted to learn more.  Payne saw that important spark we've been learning about and fanned it.  He could have told me there was no relevance in my topic, but he didn't.  He did however explain that the topic was too broad- he wanted me to add more detail and so he got me thinking and brought more "oxygen" to the process.  How about the rise and spread of Judaism?  Where was it rising and where was it spreading?  Ok, so what about the rise and spread of Judaism from it's origins to America?  Well, this continued for a week until I finally found something suitable... "The Rise and Spread of Hasidic Judaism from Eastern Europe to the United States." It's been 16 years and I still know the exact title.  As we are learning to be extremely important- it was clear, it was focused, and I knew what my paper should address.

Things continued this way for the entire semester.  I shared my writing with Payne and he shared some of his with me.  It was the first time I had a teacher share his own writing and not just give examples from previous students.  I didn't understand then how important that was, but it was another point that hit me as I worked through our module.  

Keep in mind that this was when the internet was still dial-up and very slow.  I used a card catalog to find books in the College Library.  I read the Encyclopedia.  I scoured through old journal entries and first hand accounts.  I brainstormed.  I wrote note cards, and then more note cards when Payne told me I didn't have enough.  I wrote multiple drafts.  I spent hours working on my MLA citations and completing my Works Cited page.  There were more sources than would fit on one page.  The paper was 16 pages long- all typed on the notepad program that I had available on my dinosaur computer.  

By the end of that semester I was so sick of "Pain" I couldn't stand it anymore.  The football players in the class didn't have to go through all that crap!  They also were perfectly happy with their C's.  I got an A- on that paper.  Yep, all that and I still didn't get an A.  It was a thing of beauty- but it still had a few citation errors and grammar mistakes.  Thus the A-.  I couldn't wait to be rid of Payne and his stupid 2010 class.  

It's been 16 years and I haven't been as proud of a grade since.  I still have that research paper tucked away somewhere in a box of old photos and awards.  And you know what?  Payne really was a Pain, and I love him for it.  He taught me what I could do.  He taught me that just because I could write didn't mean that I couldn't write better.  He taught me how to work.  But most of all he allowed me a sense of pride and accomplishment that I had never felt before!  Does the paper apply to anything in my own life?  No.  Did I learn a level of work and commitment that will forever aide me in my own life?  You better believe it!  Will it change the way that I teach?  Dang straight!!!

I know how to pick out those students.  Any kid can be one.  Any and every kid has something inside them that just needs to be wiggled out of them.  It might require stretching and uncomfortable moments, but that's what it takes.  They may not see it in themselves, but I will see it in them and show them what they are capable of.  I will make them work and stretch, put themselves into what they do, and be proud of the product.  It may be 16 years before they see the value, but I doubt it.  As much as I thought I hated Payne, I admired, respected, and loved him even more!

Payne gave me a good foundation, and that has been greatly added to through my SCED program.  I believe in and plan to use the following:

-Modeling work- I WILL share my own writing with my students and will make sure they are clear      on what I am looking for.  I want them to know that variety and sharing are good.

-Peer review and discussion- There was great value in the time that Professor Payne took to work with me, but peer involvement would have been an added bonus.  The learning that can take place all around when it comes to the writing process is immeasurable.  

-Building on aspects of effective writing-  My students won't be able to grasp every aspect of writing immediately, and that is good.  Scaffolding is used by teachers everyday.  It is how we teach and how students learn.  I will build my students into better writers, readers, and editors with every new opportunity!

I like the idea that was shared in this module of "Not every text a Mona Lisa."  That research paper was my Mona Lisa.  It really was a work of art!  But there were plenty of papers before that were "messy writings."  They were good, they had worth, they helped me learn different aspects of writing, but they weren't to same "level" of writing as my research paper.  THIS is the goal!!!  I want to help my students produce notes, journals, and content writings.  I want them to learn, try new things, and find a voice.  I want them to look back and see their work and the Mona Lisa that it helped them create!

Past vs. Present: The Best Way to Teach Core Vocabulary

We all remember the joy of vocabulary assignments, right?  Write the list of words, copy the definition from the text book or the dictionary, and then use the word in a sentence to show that you understand its meaning.  Boring!!!  And not just boring, but those sentences were so easy to fake- usually one was provided right in the text.  This is the ONLY way I remember doing vocal when I was in school.

This is not how I intend to teach core vocabulary that pertains to math and English to my students.  I am in a unique position where I would really like to teach classes in both of my disciplines- given this case core vocabulary word from one discipline may have a completely different meaning in the other.  

According to Harmon, Wood, and Hendrick the is a visible and invisible aspect when it comes to core vocabulary.  Students need to understand vocabulary used in each discipline on a higher level than what has traditionally been used.  Students need to be able to understand these words, apply them to concepts, visualize them, and use them in a way that demonstrates to their instructor and their peers that they are truly learning the vocabulary of that discipline.

To me the key when it comes to core vocabulary instruction in both English and math classes is simply to USE the words.  This is something I have discussed in past posts and what I plan to do in my room.  It is not enough to teach my students a word and then hope they retain it in their brain box.  I learned an interesting concept last semester that I found applies well to what Harmon, Wood and Hendrick are trying to get across.

I attended a diversity training in conjunction with SCED 3200/3210 last semester.  While talking about stereotypes, the instructor explained that we put things in boxes inside our brain.  If we come across a person that is part of a culture that we know very little about they are automatically placed in a box with limited contents.  Our brain has to categorize things this way in order to process information.  The way to change our knowledge and the stereotype that we associate with that person is to add more items to the box.  Learn more things about that person and their culture.

Vocabulary is the same way.  Just as was discussed in my last post, you need both activity and context when it comes to learning new words and concepts!  You also need to make using these words a commonplace activity.  This will help put more things in the box.  Let's talk Geometry for a minute- If I have my students write down the definition of area, use it in a sentence, and then move on to another concept they never get the actual concept of area.  Then lets say these same kids are in my Language Arts class later in the day.  I then talk to them about the area that Hemingway described in his writings.  This is a much different use of the word area and may lead to confusion the next day in our math class.  

In contrast let's say our Geometry lesson takes a different path.  We spend time discussing the width and length of an object- concepts that should be familiar to the students.  I make sure that they understand this is a measurement that we can take.  I then take a rectangle and we measure the length and width of a shape.  I take piece of paper and cut it to the same dimensions and then demonstrate how the paper covers the shape's surface.  I then explain that this is the "surface area" of the shape, it is a measure of what it takes to cover the surface.  We then practice finding the surface area of different shapes and begin discussing formulas for doing so.  This puts a lot of information in their box and meets the visible and invisible aspect of core vocabulary that Harmon, Wood, and Hendrick refer to.

In the same way, when these students come to my Language Arts class I can explain that the area Hemingway referred to was a geographic location in which he traveled.  We can both look at pictures and read his words in order to get a sense of the area.  By using these key words in the atmosphere of the class my students will better learn their meaning and be able to use them on their own making them a part of their own learning process.  This is how I will teach core vocabulary in my "areas" of discipline!