A Final Blog: Synthesis of the Course

I learned a lot from this course.  Some of the main ideas were how to incorporate comprehension instruction, vocabulary instruction, oral language, writing/representation instruction, digital literacy, critical literacy, and differentiation instruction into my own class.

I think comprehension instruction is something that should always be a focus.  It helping kids understand the math with before, during, and after instruction.  I think I will probably do a lot of lectures in my classroom about math topics, but support the lecture with a fun activity to help kids discover beforehand or stabilize their understanding afterwards.

Vocabulary is really important in math!  I hope to teach my students vocabulary well enough that they can discuss math with other people using proper vocabulary instead of slang such as replacing "when you divide fractions you flip them and then times regularly" with "when dividing a fraction by another fraction, you invert the second fraction and multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator."  I plan to introduce only a few new vocabulary words at a time, but always incorporate old vocabulary into the lessons.  The new vocabulary will be thematically related, which shouldn't be hard considering I would introduce vocabulary about the topic we are discussing.

I will always be mindful of the diversities in my classroom.  If my classroom is linguistically diverse, I will try to incorporate the different cultures and backgrounds into my lessons.  I will also try to be mindful of English language learners.  I might not do much specific differentiation because let's face it...that takes a lot of extra time: something teachers do not have in abundance.  But, I do plan to teach so that all students, even those who struggle with reading or the English language, will understand.  I will use a lot of pictures, hands-on activities, and gestures.  I will have notes available online for students to access and will write my notes on the board as I lecture.  If I do have a student who really is struggling, I have no problem differentiating so they get the help they need.  I would partner them up with someone who is doing well or allow them extra time for assignments.  The most important thing is that the students are learning math!

Writing is something I had never really considered using in my math classes before this course.  Now, I am seriously considering using it quite a bit.  I think it is a great way to understand if students are actually understanding the math rather than just learning the remote plugging and chugging into formulas.  I think it's also a great way to have students assess how they are doing.  They can see where they don't understand and where they need extra help.  Writing helps them organize their thoughts.  Representation is HUGE in math!  I plan to use graphs and drawings all the time.  I know whenever I was faced with a math problem in high school, the first thing I would do was draw a picture or graph.  This multiple representation is great for students to grasp what is being taught.

I'm currently taking my capstone class and I have learned a TON about digital literacy in math.  We have learned all sorts of programs and lesson plans to help kids learn math through digital means.  The key is to only use these technologies if they compliment and enhance the lesson.  I am not going to use them just so I can use them.  I plan to use GeoGebra a lot in my class because it is easy to create applets that will help students who are visual learners or English language learners see what the numbers are actually doing.  I also hope to stay current with what the kids are using so that I can make math fun through the technologies the students enjoy outside the classroom.

Critical literacy is a huge part of mathematics.  Students need to learn basic math skills so they can apply them to everyday situations such as balancing a checkbook, making a budget, doing taxes, or telling time.  I would love to do a unit on practical math so students can learn to apply what we are learning in class to the real world.  Also, it is really important for kids to learn how to prove things rather than just take the teacher's word that a formula works.  They need to question everything and learn how to answer their questions.

I really did learn a lot from this class.  I enjoyed making lesson plans because that is something I had never really done.  I'm getting really excited now because I can use these lesson plans that I created in a couple of years when I have my own class!  They are much more practical to me than writing an essay about some novel.  I can't wait to go try these ideas out on students!

Affective Dimensions of Reading

I don't know if I would consider myself a "good" reader because I'm not the fastest or best at comprehension, but I absolutely LOVE reading for enjoyment!  I love reading romance, fictional stories about the everyday person, and fantasy novels.  I love books that can take me away from my own problems.  I love to read the Sunday comics because they can almost always make me laugh out loud.  I love reading facebook status updates because I like to keep up with people's lives.

I always loved reading at home because I could read whatever interested me, I had no deadline of when it had to be read, and I wasn't going to be quizzed on the material.  That freedom is what makes reading so enjoyable.  Most of the time, I didn't enjoy reading books for school because I was not given any sort of choice as to what to read.  Although there were some exceptions.  For example, The Count of Monte Cristo by Alexandre Dumas is my absolute favorite book, and I had to read it for my high school English class.  I think everyone should read this book because it is so spectacular! It has adventure, romance, mystery, and historical fiction all rolled into one book!

My mom is definitely the reason I love reading so much.  She had a great selection of books in our house from children's books to adult books.  She read to me as a child and always encouraged me to read for enjoyment.  I was also greatly influenced to read the scriptures from my church group.  That definitely helped me improve my reading because there are a lot of big and strange words in the scriptures! As far as I can remember, I have always had friends who love reading as much as I do.  I remember going to the library during lunch with my friends in middle school.  We were all reading the same series of books, and we loved to discuss what was going on in our latest read.  I honestly can't think of a single person who ever discouraged me from reading.  Probably the biggest discouragement has been TV and the internet because sometimes it just seems so much easier to flip on the TV than to go find a good book to read.

I really like the idea we've been talking about in class about having a class library where students are able to find interesting books about my content area.  At first, I was thinking I'm pretty sure there are no books about math that a 14 year old is going to want to read! But, since I've been working on the text set assignment, I've found many high interest books about math for people between the ages of 6 and 600!  The young adult books often have a lot of colorful graphics which will catch the interest of young people.  They also address some of the more interesting subjects that are related to math.  I think the best way to get kids interested in reading texts about my discipline is to have them available in the classroom.

I would love to have assignments where students get to choose one of the books from the library to read and write a reflection about or create a display to share with the class about their book.  I also think it would be great to have a comfy reading corner where kids can go if they finish their assignment early.  I also think I will add little blurbs about math books in my lectures.  For instance, if we were talking about the additive identity, I might recommend that they read Zero by Charles Seife for the biography of zero.  I think these activities will foster a good climate for students to be interested in reading books about math. I think the key idea is to give students a choice of what they want to dedicate several hours to read!

When students are choosing to read for the pleasure of reading, they will probably consider themselves readers.  There is nothing I can do to make a student choose to read, but I can do several things to encourage it.  I can give them reading assignments that makes math interesting to them, maybe in a way that they never even knew was possible!  I can put in a plug for reading and how much I enjoy reading.  I can reccommend good books that I enjoyed reading at their age.  I cannot, however, force students to enjoy reading and consider themselves readers.  I hope to show student how fun reading can be and more importantly, how fun reading math literature can be!

My google books library

Connecting School and Home Experiences

As a kid I was exposed to math in the usual ways such as learning to count, learning to keep score in board games, learning fractions through pizza diagrams, and the other usual ways.  But, my absolute favorite memory about math happened when I was in fifth grade.  I was recognized for being "gifted" in math along with about five other students.  We were put into a group and allowed to "work at our own pace" in the back of the classroom while the rest of the class did their math with the teacher.  I remember feeling so overwhelmed because I didn't really understand some of the concepts.  One night I was struggling through my homework and then it struck me that because my dad was an accountant, he probably could help me figure out my challenging assignment!  I took my book into his bedroom and together we figured out the tough problems, and I was able to complete my assignment.  This is my favorite memory of math as a child because I was able to make connections between school and family.  I was able to bond with my dad while doing math!

I'm quite certain that my dad had a lot to do with the career field I picked.  I have always felt a close bond with him through math.  (Even though I have far surpassed the amount of math he ever took in school)  I grew to love math because of my childhood experiences with it.  I know that family background has a lot to do with how students feel about a subject.  If a student grows up being told by their parents that math is a waste of time, then they will probably never apply themselves in their math class because to them, it is all just a waste of time anyway.  I have a friend who grew up listening to his mom tell him how his family "couldn't do math."  He never really even tried in high school because he knew there was no point because his family "couldn't do math."  After he graduated, he moved away from home and is currently an engineering major at Utah State.  That major takes quite a bit of math!  He talks about resentment that his mom never gave him the confidence he needed to apply himself in high school.

On the other hand, my parents always expected really good grades from me.  If I didn't bring home a good grade they told me they were really disappointed in me because they knew I could do better.  But as teachers, we don't necessarily want students to do well because their parents want them to.  We want students to do well because they are genuinely interested in our subject.  We want them to thirst for knowledge and strive to do their best because it's what they want.  Well, for pre-teens and teenagers, this will probably not happen very often.  So, we as teachers must try to do the next best thing.  We must try to connect math to the students' backgrounds.  We must somehow make math meaningful for Linda by showing her that when she bakes with her mom, she is using multiplications of fractions to double the cookie recipe.  We must show Juan that when he is shooting hoops with his buddy that they are applying trigonometry to shoot the ball.  We must find out what math experiences the student already has background in, even if they didn't even know that math was involved, and show them how math applied then and how math still applies to their lives.

The state and national standards are broad enough that there is plenty of room to make connections with students' home-life to math.  The hardest part is finding out these experiences.  One way I think I might find out some of their background information is by doing a get to know you questionnaire at the beginning of the year.  It's a friendly way to find out more information about students' backgrounds and interests.  A question could be phrased, "What experiences do you have with math at home?" or "What activities do you enjoy outside of school?  Can you see any connection math may have to these activities?"  Then, you can take these experiences, and weave them into your lessons.  A story problem could be based on one student's answer to one of these questions.  That student will be able to really connect to that question, and chances are, because high schools usually have groups of students that are similar in socioeconomic standing, race, gender, interests, etc., other students will connect with that same problem too!

Another way to find out more about students' backgrounds is to become friendly with the parents.  Make sure that the parents know that math is important and that anyone can learn math.  Ask them to encourage their child to really apply his or herself.  Ask the parents to fill out the same questionnaire (only about their child, not themselves) as a beginning of the year homework assignment.  Sometimes parents can see math connections in children's home-life that the children cannot.  Some parents are more than willing to help while others want to do absolutely nothing.  But, it is worth a try because parents can have a huge influence on children, especially in the pre-teen years.

Once you have the needed background information, it is very easy to connect it to math because math is seriously related to everything!  Pretty much any interest or family background a student has can be connected to math in one way or another.  I plan to do a lot of application problems in my classroom; application problems that are actually relevant to my students' lives outside of the classroom.  Connecting to their home experiences is a great way to do this!

Math can be Cool!

One fellow student in our SCED class told me that she might have thought math was more interesting and important if her teachers had told her why math was important and how math applied to her life.  As a math major, I guess I had overlooked that because I think everyone should just understand how important math is! So here is a blog where I am writing to my future students to introduce them to how cool and useful math can be...enjoy!

http://www4.stat.ncsu.edu/~bmasmith/images/all.gif

Hey students!

Did you ever wonder why you have to take that Geometry class?  Do you find solving an equation boring?  Why do you even have to take math? What's the point?  How does it apply to your life?  I hope to answer all of these questions and more in my blog, so stay tuned....

http://mitadmissions.org/blogs/entry/everybody_loves_a_math_joke

What do you want to be when you grow up?

First and foremost, I promise you that you will use math in your future career.  Now I'm not so naive as to believe that everyone wants to grow up to be a mathematician, but math is everywhere! Of course there are the obvious careers such as accountant, statistician, or chemist, but what about one of the hottest careers these days: Engineering?

This field is chalked full of math.  Engineers must figure the optimal design for a building.  To do this, they must use a technique called modeling where they use functions to represent what they are building.  They then must figure how to optimize their building with regards to safety, time, cost, appearance, etc.  This takes all sorts of math from algebra to geometry to trigonometry!

Okay, so let's pick a career that you think will be completely safe from being invaded by math, say a rock star.  Music is full of math from the beats per measure in a tempo to the relationship of the note and its tone.

Say you want to be a doctor; yes, there is math in that field too.  Doctors must be able to determine if a person has a healthy weight by calculating their Body Mass Index (BMI).  This is basically just a formula using height and weight. Also, doctors must be able to prescribe medicine.  The amount prescribed must be determined by several variables including the size, age, and sex of the patient.

Finally, say you want to go into a career with computers.  Computer scientists have to take nearly as many mathematics courses as math majors do!  Computers are encrypted through cryptography which is a process involving prime numbers.  Computers use binary numbers instead of the standard base ten that we are used to.
Now, I could go on and on with my list of careers that use math.  So, the moral of the story is that math is really important for any career field!

Math can be fun?

There are so many cool math concepts that can cleverly be disguised as games or activities.  Check out some of these cool sites. Every time I go on a website like one of these, I end up spending at least half an hour exploring! I have also included some study sites that help with the comprehension of math concepts.  Try some! Enjoy:

• These websites are sites full of applets. Applets are basically small programs that focus on one specific concept.  They are fun programs that can help you understand a math concept better.  
• http://www.slu.edu/classes/maymk/AppletsSLUBelowCalc.htmll
• http://www.edinformatics.com/il/il_math.htm
• These are websites that can help you with comprehension of a number of different concepts in several different areas of math.  
• http://www.math.com/
• http://www.coolmath.com/
• http://www.sosmath.com/index.html
• This site has interesting math facts and fun math tricks.  
• http://easycalculation.com/funny/funny.php
• What's so special about your favorite number? Find out here
• http://www2.stetson.edu/~efriedma/numbers.html

http://www.rocori.k12.mn.us/~czechj/FOV1-00021605/

    Convinced yet?

If you are still not convinced that math is cool and relevant to your life, check out this slideshow presentation:

Why should you care about math

View more presentations from jslloyd23

Still not convinced?  I bet you will be after checking out this YouTube clip:

Now... you should have a great understanding of how math can apply to your life.  You should also see many applications of how math can be fun and interesting!

Blog Number Two: Affective Dimensions of Writing

I don't consider myself a "writer."  I have never really been able to enjoy writing because it takes me so long to organize my thoughts and to decide what and how to write. Although I don't enjoy writing, I do express myself through other facets such as scrap-booking.  

When I was in elementary school, I though I could be an author.  I even started to write several short stories or novels.  However, I never had the dedication to get further than the first couple of pages.  When I was cleaning out my old school stuff, I found the first couple of pages of a story I was writing in elementary school.  I got a really good laugh out of it!  

I still do a little bit of recreational writing;  I try to keep a journal of the most important events in my life.  I really enjoy doing this because I am free to write whatever I want because no one else reads it.  I also do the same types of writing that all typical college students do such as facebook statuses and posts, text messaging, and emailing.  I also have friends and family who are currently serving missions that I enjoy writing letters to.  

In school, I always cringed at the mention of writing assignments.  I felt they were so subjective and technical that I never actually found joy in writing them.  I especially hated writing essays for my English classes.  They always seemed like a big, dark cloud looming over my head until I completed them at midnight the night before they were due.  I also really hated writing my opinion about things I didn't really care about and therefore, didn't have an opinion on!  


Although I didn't enjoy most of the writing assignments given in high school, there were some with which I connected and really enjoyed.  When we read Call of the Wild by Jack London, we had to create a scrapbook with artifacts and letters from Buck's sled dog trainer to a relative giving an overview of the main events of the story.  This really helped me to connect with the book by using my creative side.  Another writing project I enjoyed was making a "Book of my Life" in English.  We had several specific topics such as my pets, my family, the best day of my life, the first day of high school, etc. that we had to write a page about and then we had to present the book in a creative format along with pictures.  Again, I was able to connect with my creative side and it was something that was actually relevant to me.  
        
When I am a math teacher, I don't really see myself giving a ton of writing assignments.  However, I do think it is important for students to connect math with as many different areas of their life as possible, so I do see myself giving them a few.  I definitely want to make any sort of written assignment to be something that is relevant to their lives.  I don't want them to come to hate both math and writing by making them write about something they think is incredibly boring!  On occasion, I would like to have the students write reflections at the end of lessons telling me what they understood well and what they were still unclear about. They would also write what parts of the lesson they enjoyed and what they did not like.  This would help the students express their own feelings through writing and also give me feedback for how I can be a better teacher.  I also think that I would like to have students write their own story problems when it is relevant to the lesson.  Then, they will get practice writing and using their math skills, but it will also help them relate math to the activities and subjects that interest them.  I basically just don't want to give my students big writing assignments that they will stress over and come to hate.  I also want to make sure that I assign writings that are applicable to the students lives; things that they will be able to have an opinion about and have fun writing.


Here is the sample of my writing from elementary school that I found....enjoy! Personally, my favorite part is the cliche about the birds of sorrow! ha!

Blog Number One: A Little About Me, A Lot About Math

            My name is Hailey Larson.  I am in my fourth year at Utah State University majoring in Mathematics/Statistics Education.  I currently live in Logan, Utah with my husband Zach.  We are both originally from the Marsh Valley area in Idaho.  My life is very busy because I am juggling working,being a full-time student, and spending time with my husband, but all the craziness keeps life interesting.  When I do find spare time, I love to scrapbook, watch movies, go for walks, play the wii, and read.  A funny fact about me is that my favorite animal is the goat.  I look forward to the day I own a house so I can raise a few goats!

           

          Math usually came easily to me in high school, but I didn’t particularly enjoy it.  My teachers didn’t really try to make math interesting to us; they simply lectured about formulas, math jargon, and other stuff that was irrelevant to my life.  It wasn’t until my senior year of high school when I took calculus with Mr. Libberton, who was a new teacher to our school, that I started to enjoy math.  It wasn’t all fun and games, however, because we were working really hard to prepare for the AP test.  Mr. Libberton tried to make math relevant to us.  He tried different strategies to help us learn: breaking us into groups to collaboratively solve a difficult problem, using problems with subjects that were actually appealing to high school students, and doing projects.  Although math was now something that interested me, I was very excited when I received my AP score of 5 in the mail because it mean that I didn’t have to take any math in college!  I came up to Utah State and completed my first semester math free.  Then, I realized I missed math, so I enrolled in a math class.  During this class, I realized that I really liked learning math and helping other people understand math.  I declared my major as Mathematics/Statistics Education and have been studying math for the past three years. 

           

           Math is such a great subject because it is very concrete.  For example, in English class the quality of somebody’s writing is very subjective, but in math 2+2 will always equal 4 (assuming of course that you are talking about the real number system).  Another terrific thing about math is how applicable it is to every person’s life.  I use math every day (and that is besides doing math for school).  I work in a deli and use fractions to weigh people’s food, use math to figure out how much food to cook, and use math to figure out how much to mark food to when it is placed on a sale.  At home I use math in my finances, in cooking, and in time management.  Students use math in things they love to do such as playing sports, timing musical instruments, and using technology.  The possibilities for math are endless!

            Every student deserves a good experience with math.  Our world is full of technologies that require the inventors to be very comfortable with math.  If students are not learning the basics of math or are having negative experiences with high school algebra, they are limiting themselves.  It is the obligation of math teachers to make math relevant and exciting to students.  After all, a teacher may very well be currently teaching the future inventor of something big! 

-“In most sciences one generation tears down what another has built, and what one has established, another undoes.  In Mathematics alone each generation adds a new story to the old structure.”

 –Hermann Hankel (1839-1873)

Math Quotes: http://www.math.okstate.edu/~wli/teach/fmq.html