Synthesis

As I reflect back on this class, I am so grateful for the knowledge that I have been able to pull from the lessons/readings/activities that we have had.  I have certainly learned a lot more than these 4 things that I will blog about.  I thank all of you for your comments and knowledge that you have shared with me, you have helped me grow.

Okay...The first question that I choose to blog about is this: How will you choose and teach vocabulary words?  Vocabulary is EVERYWHERE in mathematics!  Students need to understand the words, before they are expected to use them correctly.  I will choose vocabulary words that are important for the content that we are learning.  I will help them to understand the meaning of mathematical terminology by providing them many opportunities to use them in discussions and in writing. I will use student friendly definitions. I will use visuals for them to learn, such as graphs, videos, pictures, symbols, and word walls.  I will also use hands on activities for them to learn vocabulary such as foldables, matching games, organizers, and more.  These are a few of the ways that I will choose and teach vocabulary words to my future math students.

Next, I chose to blog about this:  How will you structure opportunities for students to use oral language? First off, I think it is extremely important for students to feel safe in my classroom, safe to make mistakes and safe to not know the answer and to be wrong.  In my classroom, students will be valued for their participation in class, regardless of whether they were "right" or "wrong".  I will provide opportunities for students to be heard.   I will incorporate many of the discussion structures such as the fishbowl discussion technique, partner - to - partner summary technique, and partner - to - partner drawing technique.  I will provide opportunities for students to present oral presentations, either in front of the class or with a technological medium (Educreations, YouTube, or more).  I will be careful to help students to learn math and not be "told" math.  Meaning, I will not just give them the answer, I will help them to discover the answer from knowledge that they already have.  These are just a few ways that I will structure opportunities for my future students to use oral language.

I also chose to blog about this:  How will you integrate digital technologies?  Technologies are changing every day and the opportunities are endless.  Students live in the technological era!  They know it much better than I do and are much better at it, that's for sure.  I want to include as many digital technologies as I possibly can, knowing that there most likely will be constraints.  I love Dan Meyers Three-Act Math lessons (http://blog.mrmeyer.com/2011/the-three-acts-of-a-mathematical-story/) and I plan to incorporate some of these.  I like the idea of group reports done on YouTube, Educreations, or a Glog from Glogster (I created the Glog on the left...so fun).  Desmos provides many opportunities for lessons and projects as well.

 

 

Last, but not least, I chose to blog about this:  What kinds of texts will you make available to your students?  As I worked on my Text Set assignment, my eyes were opened to the amount of texts that we can provide our students with.  I also started thinking about the math classrooms that I am in everyday and I've never seen a "library" of math texts for students.  Why not?  I love the idea!  I will include many texts in my library for my students, magazines (my favorite was MATH - the Scholastic Math Magazine), videos, apps, book, websites, and more.  But, also...outside of my math library, I will use many of these texts within my classroom for lessons, activities, assignments, and more.  I hope to have a classroom where learning happens and we can get down and dirty in math problems, but also learn in fun and inventive ways...incorporating these fabulous resources that are so readily available to us.

For fun and a smile check out this fun movie of Donald in Mathmagic Land...

I have learned SO much in this class...I didn't plan on that, many of the techniques and strategies for teaching I never knew existed.  Thanks for the opportunity to learn so much this semester! :)

Oral Language

For my job, I get to observe 8 different math classrooms/teachers.  As a benefit to this job, I get the opportunity to see how different teachers structure oral language with their students and what seems to work (or not) for each teacher.  I learn from all of the teachers that I am assigned to.  However, there is one teacher that I mostly learn what NOT to do...  We are going to call the teacher whom I would like to write about, Mr. Z.  

In Mr. Z's classroom, there are many students who don't talk, because it isn't welcome most times in this classroom.  The overall feeling of the classroom is negative, unsafe, and not a great place to learn.  Unfortunately, students don't feel that they are valued in this room, understandably.  Needless to say, Mr. Z hasn't structured many ways for his students to speak in class.  

Recently, there have been many visits by the Principle, and Mr. Z has begun a special course at the school to help him correct his teaching/classroom.  Mr.  Z has begun allowing students to work together to logically solve real life math problems.  He then chooses a group of students to come to the board and explain to the class what they did and how they thought through the problem.  Mr. Z is now praising not only the correct answers, but also the incorrect answers in a way that the students are beginning to feel safe to make mistakes.  This makes me happy.  All students should feel safe to make mistakes or not know the answer...

Here is what I would begin with to help Mr. Z (in addition to what he has already been working on with the Principle)...  I would suggest to Mr. Z, that he add in a few more discussion structures.  The three that stood out to me in the reading were the fishbowl discussion, partner - to - partner summary, and partner - to - partner drawing.  The fishbowl discussion is similar to what he is doing with the students at the board, only this way the class will hear their discussion from the beginning.  I like this one so that students can see how others process a problem in their minds (similar to a think aloud).

With math being a subject with many algorithms, I can see how the partner - to  - partner drawing technique would work great (with more than just algorithms).  Students could sit back to back...one student could sit with a mathematical problem all worked out in steps.  They could explain the problem using steps to the other student and vice-verse.  The idea given in the reading was excellent too!  Having a student explain a geometric figure using all of their description words helps them learn their vocab.  I love this one!

I would also tell Mr. Z to find the value in his students, he has such an incredible opportunity to make a different in each of his students lives....they need to feel welcome, valued,  and safe in his classroom.  I truly feel that if he got to know his students, even just a little bit he would see the great potential that they all carry within them.  These are great students!  Talk to them Mr. Z and them be heard.

Critical Literacy

Within my content area I recently had a teacher who fostered critical literacy in one of my statistics classes. This was my first stats class and I was only just beginning to understand statistics. She taught us to think through the experiment that we were reading about to determine if they were a reliable experiment or not. She taught us the important steps to creating a reliable experiment first so that we knew what to look for and so that we would be able to recognize when something wasn't quite right. Then, she asked us to go out and find an example of a reliable experiment and also to find an example of an experiment that wasn't reliable and of course to explain why on both. We were asked what we would do to “fix” the experiment. We were asked if we would “believe” this experiment.

One of the articles that I read was entitled, An Introduction to Critical Numeracy by Rex Stoessigner. The article lists four major aspects of critical numeracy. (1) Being able to critique or make critical interpretations of mathematical information. (2) Being able to unpack, interpret or decode mathematical situations. (3) Using math in a self-reflective way. Lastly, (4) Using math to operate more powerfully in the world. I think that this is powerful, for students to be able to develop their own healthy skepticism about the use of mathematics in the real world. This article gives an example: Paying the price for saving. It talks about a man who purchased every item individually to save money (based on a store policy with rounding the price of the item). After the example, the article talks about some different critical numeracy questions that a reader/observer/student could ask themselves to better understand how to feel about it in the real world (to gain a healthy skepticism about the example). This was very similar to the assignment that my stats teacher had assigned to us.

I would definitely like to teach my students how to use critical numeracy/critical literacy in their lives. It’s important for students to feel empowerment within themselves and if I can accomplish that through teaching mathematics…that will just be amazing.

Digital Text and Reflection

I decided to check out 2 different digital texts...not to go the extra mile, but because the first one gave me a headache trying to work with (at first).  After some trial and error...I decided that I really liked BOTH digital texts.

The first one that I worked with (and struggled with a bit...only in the beginning) was from the webpage, http://edu.glogster.com/.  You have options to create your own handouts, assignments, posters, biographies, book reports, and so much more.  There is also an overflowing handful of these items already created by gifted educators that you could use for your class.

Here is the glog that I created...

Here was the process...  You get to choose a template.  You can edit everything on the page.  You get to add video (mine actually works when you access the glog instead of just the picture above), images, graphics, web-links, audio, and text.  You get to choose where you want everything, how you want it to look, etc.  It was really a fun thing...once I switched to the iPad.  Note:  The iPad app was MUCH easier for me to manipulate than the computer.  Next time I will do all my work on the iPad and NOT on the computer. Plus...it would help if you watch the tutorial.  I just found out that there was one (ha ha).

Technical issues aside, I think that it would be very fun for students to create math projects on Glogster.  The sky is the limit here.  Here is just one idea:  Ask students to work in groups to create a poster that corresponds to a standard that the class has just learned.  I feel that going through the process to find images, text, videos, etc., will cement the standard more firmly in their minds and help their understanding to deepen.

The article that I read explained that Glogster is a great tool for students to be actively engaged in their learning  Students get the opportunity to use think aloud strategies.  The article did state that Glogster is a social networking site and permission would have to be granted for students to use this site.  It also stated that students can have trouble finding photos and text that they have in mind.  It stated that the teacher should model for the students how to go about this process before requesting students to create a glog.  It also talked about how to create a rubric for an assignment created on Glogster since it could be difficult if students aren't tech savvy.

The next Digital text that I played around with was the app called, Educreations.  I found this app on my ipad.  There is also a web page here, https://www.educreations.com/.  The following link is a video that I created on solving systems of equations with the elimination method.  It was fairly simple to create using a stylus, the text ability, and a photo of a grid to graph with.  I learned one important thing about myself...I need to talk FASTER.  I was talking so slow that when I watched my video for the first time, I was wishing for a :"speed up" button, ha ha.  Next time I will keep that in mind.

https://www.educreations.com/lesson/view/systems-of-equations-elimination/29654383/?s=HKkN3d

The process was very simple.  I could pause/record whenever I needed.  Writing was simple, attaching a photo was simple.  The only problem with the program was that you couldn't rewind and re-record a section.  There were a few places where I stumbled in my (slow) talking or where I made an error that I wished I could have gone back and changed it.

I think students would love this!  One idea would be to ask students to create their own storyline for an exponential function (this could be either exponential growth or decay).  In addition to the storyline, ask them to write the exponential function that corresponds to the storyline, graph the function with labeled axis, and explain what the realistic domain and range of the function would be.  All of this could be done with Educreations.  This was much more simple than a glog from Glogster...although Glogster produced a much more fun product.

See you next time...

Writing Instruction

I enjoyed writing assignments that had topics in which I could relate to, had an interest in, or felt passionate about. These were my favorite types. My absolute favorite writing assignment was a very personal essay in which we were supposed to write about events from our lives that have shaped who we are today. This was a very emotional essay for me to write and so personal that in the end I wasn’t sure if I wanted to submit it or not. I truly enjoyed writing it because I really had to dive into feelings about my family and my parents’ divorce. This essay required me to remember feelings I had growing up…it was interesting how I could recall my childlike feelings from years ago. Bringing these feelings back to my mind also brought adult like questions and a new perspective as an adult; I was able to almost feel/see my mother’s emotions from this earlier time in my life. I really enjoyed this and began to feel much closer to my mother. This teacher taught us to take a piece of paper and just quick write random thoughts, memories, and ideas that came to our minds. While doing this I was amazed at the overload of feelings and memories that came to mind, even though much of it brought back sad memories, it also brought back many fun and joyful memories. I loved this assignment mostly because I was able to write about something that meant so much to me. I also loved that I was able to express myself in my own way and in my own words.

I didn’t like the assignments that were on topics that I didn’t know anything about, had little to no interest in, or those that had so many specifics that I couldn’t make it my own in any way. I had to write a research paper once on an ancient artifact in my Civilizations class…I did NOT like this paper. There was little information on this artifact and I didn’t have enough information for an entire essay. I really struggled putting the information into my own words, so it was difficult to not just copy the sentences word for word. Also, I hadn’t taken my English courses yet that taught me how to properly cite phrases, etc. This made it very time consuming and difficult to do this portion of the paper. All in all…I was happy to be done with it and I never wanted to write about something so boring every again.

From the reading for math majors, I liked how Steele explained that writing can help students understand their lessons in a much deeper way that simply knowing the algorithms to solving problems. This helps them to develop a deep conceptual understanding. I love this! It makes me excited to incorporate writing in my math classroom. This is a piece that I feel is different from when I was learning math. When I was learning, we were taught the algorithms so much more than the “why’s” of math, we were formula and memorization kids. I feel like now we are being told to teach this new way that we weren’t taught. It’s exciting that writing can help us accomplish this. I loved the example that the reading gave of the intermediate school where the students were asked to write a recipe for solving various problems, what a fun assignment. I completely agree with their math department’s mindset that “whatever you do in your life, you need to present it in an oral and written form.” I know that students will ask…why? They always do, right. This is a great explanation.

I think writing should be a permanent part of a math assignment. Our students should be able to explain in words what they are doing with numbers. For example, when they write a function, they should be able to explain what each piece means, instead of just (y = 99x + 50), they should also be able to say (The total cost of a plumber visit is equal to $99 per hour + $50 just for coming out). This helps them to understand exactly what each piece of the equation actually means.   This will help them visualize the graph of the function as well. Below I have included the graph below for fun, you can create these on www.desmos.com (this is a really easy and fun graphing website to work with).  A student would be able to see that no matter what, even if the plumber only comes for less than 1 minute, the cost will already be $50, if he stays for 1 hour, it will cost $149 and so on.  It’s so important for students to write about math, I plan to include this in most of my lessons/assignments.  I can include simple writing prompts like this one and also longer assignment like the essay that the students worked on from the reading.  There are endless opportunities for writing in math.

Vocabulary Instruction

Hello all…I am on cloud nine this week because I officially have applied for student teaching this fall. It’s been a slow and steady race. I feel like I am the tortoise in the story of the tortoise and the hare…so many have surpassed me and have already graduated. But, it’s just right around the corner now. Yay! I can’t believe how close the finish line is for me. We all are going to be teachers soon! J

Last semester I had a fabulous teacher name Kami Dupree. During one broadcast class, we were asked to print a sheet of paper with different sized and dimensions of rectangles. We were asked to group them in whatever way we saw fit. Then we were asked to explain our reasoning for why we grouped them that way. Eventually, through class discussion we formulated a definition for the math term of similar without knowing that this was what she was trying to teach us. We gave our ideas, she wrote them on the board, and eventually came up with the definition. I loved how she did this. Not only did the lesson catch my interest and kept my attention, but it helped me to understand and know the term of similarity at a deeper level.

I definitely agree from the reading of Harmon, Wood, and Hedrick that mathematics text can often have different meanings in math than in everyday life. It’s important to teach our students the meaning in mathematics since they most likely won’t hear these words with the appropriate meaning (for math) outside of school. Our students will be able to learn a concept so much more when they understand the words and what they mean for math. As we help them to understand the wording, our students will build upon knowledge from the past and gain a much deeper understanding. I find it interesting that they mention that content area instruction in word-learning strategies is especially important for those students falling behind. I guess if you think about it though…if you didn’t understand or know a language well, it would be very difficult to understand and you would fall behind. I would replicate my previous teacher practice for sure…she did an amazing job. I will also add in more of the techniques that we have learned this week. I can see how extremely important teaching text really is. I never realized this until now.

Comprehension Instruction in Math

When my teacher in High School was teaching me about geometric sequences, I remember him first giving a brief reminder of what arithmetic sequences were…which we had learned before this time. My teacher gave us an arithmetic sequence problem on the board (something to do with simple interest) and asked us to find the first 5 terms and the recursive formula for the problem. He gave us time to work through it while he walked around the room answering individual questions and observing how well were remembering and if we were comfortable with this previously learned knowledge.

Next he brought us back into the classroom discussion and went over the problem on the board. He then gave a 5 minute (or so) lesson on geometric sequences basing this on the same problem that we had just done for arithmetic. He showed us how these two were connected and how we could go from the arithmetic sequence to the geometric sequence for this problem.

This particular teacher would often ask us to take a moment to think about what he had said, so that our minds had time to process, understand, and/or question. He would ask us to write questions down as he lectured…otherwise we would forget them. He often would use think aloud strategies with us. With this lesson I remember him talking about finding the value of r, the common ratio. For example, if a person had deposited $100 and this $100 would gain an annual interest of 6%, I remember him saying that he first thought to let r=.06 (since this is the decimal for 6%), so after the first year the person would have earned $6 in interest… But, then he mentioned that he wanted to know how much money would be in the account at each year, so he explained why we should let r=1.06 instead…this way we would know that there was $106 in the account after the first year. He was really great at explaining what he was thinking. He would often pose questions…for instance, he would say, “what should I do next” or “where did I go wrong”. He was great at letting us think instead of him just telling us the information.

Thinking back on this teacher I will use a lot of his strategies for comprehension instruction. I love that he would connect our prior knowledge to new topics that he was introducing (One of Buehl’s processes). I love the think aloud strategy, it made me feel like he had to work for the answer too and that he wasn’t just a math machine that knew all the answers. I will use his moments of silence to think about what was just taught. This teacher also drew a lot of pictures, diagrams, and tables (also a Buehl process) that I will use…to me it’s much easier to understand if you can visualize it. I like that he told us to write down questions throughout the lesson (Also in Buehl), I will do this as well. What I think I liked the most was that he didn’t just lecture; he asked lots of questions and helped us to lead the lesson through our own thinking instead of simply being told. It was okay to be wrong in his class…he always praised us for trying.

Just in case I sparked your "interest" into figuring out interest...here is a link to my very favorite math geek explaining simple and compound interest...he is my hero!

Introduction

My name is Megan Dangerfield.  I have been in school for what seems like an eternity...7 years.  I started when I was pregnant with my littlest one and needed to sit sideways in the seat because of my pregnant belly.  My super supportive husband has been amazing all this time.  We feel like we have both been in school.  He definitely deserves a diploma in the end after balancing family, school, work, and everything else with me...it hasn't been easy.

When I started school I had no clue what I was going to major in.  I went in completely blind and tried to follow my heart.  I loved math and kept taking math courses as electives, my friends thought I was crazy...my family knew that I was.  After Calculus 1 it hit me and I realized how much I wanted to help others love and learn math.  Ever since, my future has been known.  After 7 years I now only have this semester and my student teaching left until I graduate with my Bachelors degree in Mathematics/Statistics Composite Education. I have chosen jobs along the way that have prepared me to become a math teacher.  I was a math tutor at USU for three years, a substitute teacher for just over a year (mainly in high school math class), and now I am spending my days at the High School as a math tutor.  I LOVE it!  I love the students, I love the math, I love the entire atmosphere.  I can't wait for my future to become reality for me...and it's just around the corner. :)

My family is my everything.  I said before, my husband is amazing, he is my best friend and my greatest support.  While I am at school, he is home helping with laundry, cleaning, homework, dinner, baths, blow drying hair, singing bedtime songs, reading stories, and so much more...and this is after a full days work.  He is incredible...I am one lucky girl.  We have four children and they are fabulous!  Each one is completely different and I love them all for their differences.  This year was an interesting year...my first baby started High School and my last baby started Kindergarten.  My oldest is 15 and my tiny little one is now 5.  Being a mother is the hardest thing I have ever done and also the most worth it.  I keep very busy between late night baseball and softball games, football, dance, family movie nights, glow in the dark wiffle ball games in the street, shopping with my girls, dates with my best friend, and so much more.  Life is good.

This picture was taken back in the Spring of 2012 when I earned my associates degree.  I can't wait to see how different this picture looks when I earn my bachelors degree next year (my family is literally growing up during my schooling).

I looked up the exact definition for literacy.  The definition means two things.  First, literacy is the ability to read and write.  Second, literacy is the competence and knowledge in a specific area.  For math, both definitions are important.  Math is not simply numbers, there is so much reading and writing.  It is extremely important for students to understand mathematical terminology so that they can understand what they are learning and know how and when to use each concept.   Also literacy in mathematics means the knowledge and successful ability to "do" math.  Every math student should leave from math class with a greater literacy for math...this is my goal.  I hope for all my future students that I can instill within them a desire to learn math, a greater confidence in themselves to try, and a more positive attitude about math in general.  I hope to math learning math fun.