Math as a Language

The first blog post I wrote was how to become math literate and what it means to be math literate. Expanding on that, this post will be about math as a language. Math can be a challenging subject for students now and again. Students have to learn new terms and symbols for the language of mathematics. There are some ways in which students confuse math as a language and there are different ways in which educators can guarantee that their students are able to understand the language of math. For students to develop mathematical literacy skills, educators can utilize guided talk and graphic representations. In the classroom, educators can offer direction on utilizing research to improve math instruction. Student-centered learning and building concept related skills are a significant aspect as well for students to develop their mathematical literacy skills.

The languages in the world share one thing in common, which is, they have a classification for words like nouns and verbs. This gives an intriguing method for looking at math as a language. Mathematical nouns represent things such as numbers, measurements, shapes, functions, patterns, and data.

The language of math was arranged in a way so we can write about things like numbers and functions and what we do with those things such as adding, subtracting, etc. Instead of words, math typically uses symbols. Some symbols may include the ten digits, operation symbols (+, =, -), variables like x and y, and special symbols like < or “pie”. Sometimes the alphabet can have special uses. The start of the alphabet is typically used as constants in a problem and the end of the alphabet is used as variables for an equation. Nouns could be fixed things such as numbers or expressions with numbers. The verb could be the equals sign or an inequality symbol. Pronouns could be the variables of x and y. Finally, everything can then be put into a sentence: 4x+9=16.

 

This past summer, I was able to study abroad in Ireland for a pre-student teaching experience. I was placed in a 4th class classroom, which would be 5th grade in the United States. When they would work on math, which they called Maths, it would be a little different than the United States. It caught me off guard when I first heard the word Maths because it was something I was not used to at all. The language that they used was worded a little different than how we say some math related things in the United States. Some of the phrasing was different than I had learned, but it was still overall math terms. I was very grateful to go to Ireland and have this experience in a culturally different classroom than I have been in before. It was eye opening to see a subject I love be taught in different ways, yet globally use the same basic math language.

As you can see, math has its own terms and symbols that are only used in math. If someone does not have developed math literacy skills to understand the language, they would have a hard time doing any problem solving in math. For students to succeed in math, it is so vital for them to understand the language used in math and many students might not realize that in the beginning. As educators we need to make sure students are learning the language to achieve success in math.

Shifting Practices (pt.1): Responsive Approach

img_5091A major way my teaching practice has shifted* is in the way I attend and respond to my students’ thinking.  I am more focused on a “Responsive Approach” in my classroom which is guided by my students’ interests and needs both academically and socially.

(* Interested in seeing the “Ignite Presentation”(what is that?) I made to accompany my reflection of how my practice has shifted? See it here “Ignite” photos.)

Students learn best through social interaction.  However, they need to be explicitly taught social and emotional skills.  Modeling how to play games in a group is just as important as learning the academic skill practiced in the game.

I’ve learned to step back and observe when students have disagreements to help them develop and practice problem solving skills.  Then, in class meetings, we discuss solutions to problems that we’ve observed.

Giving my students more opportunities to practice these skills has helped foster a more inclusive environment.  I’ve implemented several different social experiences such as “play buddy” partner games, “listen and tell” story time, and the “let’s talk it out” friendship bench.

Integrating family participation in our classroom is another way I have focused on becoming responsive to my students’ learning.  One of my English Language Learner student’s parent comes in weekly to read a familiar book in Spanish to our class.  

Inviting parents in to share a story, help with our monthly cooking days, teach a song, or assist with a hands-on lesson are just some ways I am focusing on building a bridge from home to school in my students’ lives.  It is important to find ways to partner and involve my students’ families in our learning.  These partnerships help strengthen our classroom community and enrich our school culture.

From across the classroom one day, I observed some of my students taking “selfies”. Granted these were with old “wind and advance” cameras, but it reminds me of the need to be responsive to my students’ inquiries and multimodal literacies.

Responsive teaching aligns with the idea of scientific practice.  Letting my students experience cause and effect and figure out how something happens in their own investigations is another way I have shifted my planning.

I am now realizing that I do not necessarily have to incorporate fancy technology tools to engage my students in multimodal activities.  I am providing various materials and asking questions to engage my students regularly in multimodal literacies.  Moreover, I am more knowledgeable in digital literacies and connected with external networks to get inspiration and to continue learning.

Being responsive to my students’ questions,  ideas, and observations has led to more excitement and confidence in our classroom.  My role has shifted from being the giver of knowledge to supporting, watching, and listening to student’s thinking to guide my lessons.

Like when my students showed great excitement over using a trail map on our field trip.  I followed this spontaneous opportunity to reshape our curriculum.  Although I had planned a different unit, I forced myself out of my comfort zone to try some new lessons to keep my classroom a community that is shaped not by my agenda, but by my students’ interests.

I continued to take the lead from my students’ questions about maps as we learned and practiced position words, drew maps of our classroom and routines, and went on a bear hunt in the dark!

Furthermore, after discovering my students’ obsession with superheroes, I used this theme to frame a positive self-concept unit.  We all can be super and have different powers that make us each unique.

Recording my lessons, receiving feedback, and reflecting on my students’ learning resulted in more intentional modeling.  Demonstrating my own participation in literacy through modeling is supporting my students’ development of these skills.

Modeling and giving students examples of why we use text and relating their own experiences to help them make connections is another way I have shifted my practice.  I find myself asking, “How can I show them this concept through their eyes?” to make it meaningful.

My focus is to encourage all attempts at reading, writing, and speaking by involving all my students varying abilities in literacy practices.  

Labeling pictures and events with marks or letter sounds or words is one way to accommodate all my students’ levels.

Finally, I have changed my focus from product to the importance of process.  My students are more involved in sharing their story ideas, talking about their observations, and learning through each other.  Being more in-tune and responsive to my students’ thinking is providing a more positive learning environment in my classroom.

* Interested in seeing the “Ignite Presentation”(what is that?) I made to accompany my reflection of how my practice has shifted? See it here “Ignite” photos.

Coming Full Circle with the 20% Project

This week I had the opportunity to hear Kevin Brookhouser speak AGAIN about the 20time project in his classroom. I even got to meet him! I had heard him speak at a conference in July and hearing him speak again really brought the 20% project I had implemented into my 2nd grade classroom come full circle. It left me inspired again and gave me a new route I would like my 20% project to take.

Many of my students are now finishing their 20% projects and are starting to teach the class. Last week I had my first two students present and I was blown away. The first student taught the class about algebra. When he first told me he was researching this topic I was very apprehensive and did not know how he would be able to teach the class about such a complex subject. To my surprise, he did it perfectly. He made a video on Seesaw in which he described why he loves algebra and why he wanted to teach the class. Next, he made a poster in which he did an interactive presentation. He explained how letters are used in place of numbers to figure out the problems and that the problems are like puzzles. The students were instantly intrigued and were engaged as he gave them problems to solve together.  His first problem was x+3=6. As the problems progressed they got a little harder and he then explained that it takes a lot of practice to understand it.

 

The second student that presented taught the class about one of her passions, gymnastics. She made a poster where she explained what she wears and where she goes to practice gymnastics. She then showed the class some of the gymnastic moves she has been practicing and they loved it. It was so exciting to see her passion shine through as she taught her fellow peers.

Seeing their success has lead me to my next goal for this project. I want to bridge learning with passion, which is why I originally started this project in my room. When I heard Kevin Brookhouser speak again he was talking about how this may look in the elementary school classroom. He suggested that if you want students to create a solution to a problem and gain a sense of empathy then the teacher should facilitate the class in solving a community problem. For example, students could learn about nursing homes and build a relationship with the people that live there. During the 20% class time students would create, publish, research, and write to solve a problem for the nursing home. Maybe they could create cards or pen pal letters with the residents. They could also create things to give to the residents, etc. Once you do a 20% community project, students could then try to solve a problem they see in their own community. Whether it be teaching younger students, creating videos to help the school, or raising awareness for charities. As students finish up their first 20% projects we will start a project as a class. I hope my students learn how to be problem solvers while also letting their passions shine through and giving them a purpose for their learning. This experience has completely changed my outlook towards teaching and my classroom.

Are Vocalists Better Musicians?

What does it mean to be a “literate” musician? This question has been on my mind recently. 

One of my best friends in the school of music and I frequently have conversations about philosophical (and political) issues. In a recent discussion, we talked about some stereotypes about different kinds of music majors, particularly vocalists. Vocalists tend to struggle with rhythms and music theory, because they do not regularly perform scales (and such) the way that instrumentalists do. He then told me that he thought that despite this, vocalists were better musicians than many instrumentalists. When I asked him to explain why, he told me that in vocalists’ lessons, they often spend time just improvising; they create music on their own, and they do it easily compared to instrumentalists’ improvisation.

 

This got me thinking: is music literacy all in the theory, or is it solely in the application? The truth (obviously) is that it comes in a mixture, and this can make it difficult to define what it means to be a literate musician.

 

I believe that as musicians we have two sets of vocabulary. The first set is the theory. This is knowledge of scales, rhythms, and meters. This vocabulary is measured, and it allows a musician to excel in reading written music. This is important, given that music, unlike many other art forms, is largely performing music that others have written and performed countless times before. This is the “left brain” section of musical vocabulary. It also is composed of technical fluency: the ability of the fingers, tongue, mouth, throat, etc. to produce the sound on the instrument (or voice) the musician is using.

 

The second set of vocabulary is creation and emotion. This is the inner ear that sets thoughts, feelings, and imagination to notes and chords. This is the ability to improvise countless new melodies in different harmonies; it’s the musician’s “right brain”. This section of the vocabulary is also important to interpret existing music in new ways: should this note be played shorter or longer? Should the line crescendo here?

 

Musicians need both of these “vocabularies” to be successful. The truth is that all good musicians, instrumental and vocal, possess these vocabularies. The issue comes in the integration of the two vocabularies. How does one get the music they hear inside out into the world? This is the answer to why my friend thought vocalists might be better musicians: to them, this is innate. The voice is such an integral part of who we are as people that the vocalists naturally integrate these two vocabularies; they can sing out exactly what they hear inside. The challenges of the instrumentalist are how to translate what they hear inside onto an instrument. This requires mastery of the technical vocabulary of the instrument, but we see this mastery in many musicians, especially in the jazz scene.

 

So how does this play into being “musically literate”? A comparison can help here. The first set of vocabulary (the theory) is like a person’s actual vocabulary: the words they know and their grammatical knowledge. This allows them to read text, and it allows them to create their own. The more sentence structures, words, and stylistic elements they know, the better they will be able to write. The second vocabulary is the ideas. These are the thoughts we all have in our heads. Many of us have experienced “writer’s block”, but this often isn’t so much a matter of not having any ideas but of not having the vocabulary or knowledge of sentences to put these ideas into words. Many students struggle with this; they are quite intelligent, and they have ideas that could make a coherent paper or story, but they lack the technical vocabulary to actually write it down. This is the struggle of the instrumentalist! Instrumentalists may have a plethora of musical ideas, but unless they have mastery of the “technical vocabulary” of their instrument, they are left unable to make their ideas into a piece of music. Vocalists are able to simply speak their ideas directly, much like if a student simply said their ideas however they came into their head.

 

I think that any truly great musician must have a breadth of experience and talent using both of these vocabularies. The truly amazing musicians, though, will have an amazing ability to use their technical vocabulary to express their creative and emotional vocabulary. Instrumentalists can only accomplish this through mastery of the technical vocabulary! So in other words, while vocalists may seem on the surface to be better at integrating these vocabularies, that is because it comes much more naturally to an instrument as personal as the voice.

Getting Engaged Through Big Universe

Every once in a while, teachers receive that dreaded e-mail: “You are getting a new student.”  Now don’t get me wrong, I absolutely love the kids I teach and after meeting the new student I quickly grow to love them too.  But the inconvenience of finding a place to sit, getting them caught up in the curriculum, the unknown of behavior problems, past history, etc. causes some anxiety.

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Well back at the beginning of November, I received this e-mail.  Instead of the typical quick fact sheet, I received a note in my mailbox telling me to see the school data manager about this child. Great, I immediately thought, this child has so much baggage the report won’t even fit in my box. 

On my lunch break, I headed to her office bracing myself for whatever I was about to hear.  It turns out this new student of mine has quite the past indeed, but not in the way I was expecting.  It turns out he has been abused pretty terribly at home and now has a restraining order on one of his parents.  He is extremely below grade level and very hesitant to participate.  He has been enrolled at eight elementary schools so far and it’s only fourth grade.

My mood immediately shifted.  Instead of worrying about where he would sit or what cubby number he would take, I realized there were much larger issues here.  His first day came the next day and he very quietly walked into the room.  He didn’t talk much and wouldn’t make eye contact.  Getting him to participate in anything was a struggle.

He has an IEP, so he would be getting quite a bit of additional support, but unfortunately this took a couple weeks to get put in place and he spent that time in the grade level classroom struggling to get any work done.

The last thirty minutes of our day is called “YET” time.  This is when ESL students are pulled, intervention groups push in and pull out students below grade level, I do guided reading groups, and the rest of the students do stamina reading.  This boy also happened to come back from his CCR class at 3:00.  He was too low to be in my guided reading groups, and he isn’t ESL so that wasn’t an area he could be in either.  This meant that he was to stamina read for half an hour every day.

The first day I went to my classroom library with him and we looked at books on his level and tried to pick out one that interested him.  We finally made a decision and he went to his spot to read.  As I was reading with a group of students, I noticed he had the book in his lap and was making a paper airplane on top of the book – clearly not reading.  I let it go this time.

The next day, the same thing happened so I went over to tell him it was okay to pick out a different book if he didn’t like that one.  He went over to the bookshelf, picked one out and sat down.  This time I noticed him coloring instead of reading.  I was uncertain how I was going to get this child to read at stamina reading time.

Then I remembered Big Universe.  This is a program my county pays for and it allows students to read books online that they get to choose.  There is a huge database and they can find books at their level that interest them.  They can even put headphones in and have the computer read the book aloud to them.  I figured this was worth a try.

big-universe

The first day I had a student help him get logged on and he seemed to really enjoy it.  Every time I looked back at him he was staring at the computer screen with his headphones on, totally oblivious to the things happening around him in the classroom.  The next day, he came up to me after and told me how he read about sharks and some cool facts he learned about them.  I couldn’t believe how engaged he was!

It’s important to get to know your students and realize that something that works for one student may not work for another.  This child came to me very quiet and reserved, and now he actually gets excited to share with the class things that he read about.  Sometimes getting a new student can actually change the way you view your teaching.  I know that he has taught me a lot already in his month here, and I can’t wait to watch him grow even more.

Time to Unplug

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Last week, I made a commitment to unplug for a few hours each night.  Honestly, I didn’t go all out on my commitment.  For example, I didn’t pledge to stay away from all social media, all day for the whole week.  I knew that would be difficult impossible.  So, instead, I chose to stay away from social media in the late evening.  I didn’t think it would be a problem for me to put away my phone and/or computer for a couple of hours each night.  I was wrong, very wrong.  It was extremely hard to unplug even for a couple of hours each night.

Here’s how it went.  The first night, I told my husband what I was doing.  I announced, “I am not going to use social media tonight from 9:00 – 11:00 PM.  In my mind, social media was Facebook, Instagram, or Twitter.  He was happy and quickly started a video he wanted me to watch that had been shared with him.  After 15 minutes, it suddenly dawned on me that YouTube might be Social Media.  So I quickly grabbed my computer and googled, “Is YouTube S… Before I could even complete the “S”, up came “Is YouTube Social Media”.  The answer was a resounding “Yes”.  My first day was a “fail”.

Day two was difficult because I had not had time during that particular day to check Social Media and kept reaching for my phone in the late evening.  I felt like an addict, reaching for my phone and putting it away over and over again.  I made it through that evening without getting on Social Media, but I decided to go to bed early, just so I wouldn’t have to think about it.

After the first couple of days, I was able to fill my evenings with much more valuable projects and activities.  One night I finished reading a book I had started.  Another night, I spent time cooking to get ready for the Holiday, one night I played cards with family and then on the final night we went to a movie.  After three or four days, I didn’t crave looking at social media and I felt a lot better about how I spent my time.

There were a few important lessons I learned while trying to unplug from social media.

  1. Social media is everywhere.  It’s not just Facebook, Instagram or Twitter.
  2. Unplugging is hard. Checking social media is ingrained in us.  We check it too often and ignore the people and relationships right around us.
  3. We can recapture quite a bit of time for all the things we say we don’t have time to do. Reading, talking, painting, meditating and listening to music are worthwhile activities and after being unplugged, I had time to do those things.
  4. Spending time on social media is a big waste of valuable time. I was able to enjoy 12 extra hours of downtime, since I unplugged from social media last week.

Last week I unplugged because of a class assignment.  I don’t think I would have seen the value in unplugging without actually HAVING to do it.  It’s hard to grasp how much time we waste while being constantly plugged into our phones and computers.  Last week I unplugged because I needed to complete an assignment.  This week I will choose to unplug in the evening.  I have a lot of things I want to do.  Charles Buxton said, “You will never ‘find’ time for anything.  If you want time, you must make it.  Unplugging for a week helped me to make time.

 

Blogging; The Word I Fear

All semester I have been thinking about what I should write my blog post about. As I began to think about writing, I became scared of writing a post. My hands became sweaty, I became nervous. My head begins to fill up with thoughts. Will my post make sense? Is my comma in the right spot? Is that the word I want to use? Will people like what I’m saying? I’ve thought about writing so many things but have shot them all down sooner than I could really form ideas about what to say. I am so scared of writing on the internet that while I do have Facebook, I have yet to make a Facebook status. Facebook posting comes with fear as well, many of the similar fears that came up when I began to think about blogging.  

The fear to write a blog is something I struggle with. Why would writing something make me so scared and paranoid. I write all the time for my classes. The thing that makes this so different is I cannot control who sees it. Writing isn’t something I find easy. Writing is my weakest subject, I am very insecure about my writing. The idea of taking something I am insecure about and publishing it for all to see is terrifying.

So here I am making my first blog post. Did I overcome my fear? Not really; but I had no choice, I either make the post or lose points. I did however; become slightly more okay with the idea of posting. Before I made my post, I spent some time on google learning about blogging and reading about others who have the same fear I have. A lot of websites talk about blogging about subjects you are confident on or know a lot about. What better thing to write my post about than something I know so much about; the fear of blogging.

The fear of blogging is very real and many people struggle with it, it is something that will take time to fully conquer. Taking the leap and going out and finally making a post is my first step at overcoming my fear. Over time, I may be a confident blogger, but time will only tell us if I will be a confident bloggerblog