"Coming together is a beginning; keeping together is progress; working together is success."

---Henry Ford

Working together is the goal of my mathematics classroom. Rich discussion and friendly critique provide an engaging and rigorous classroom. While this is my goal, I have found creating it to be a learning process in and of itself.

First I bring my students together in the classroom by arranging their desks into tables. Listening to each other I liken to keeping together. This I also have to teach. Students don't necessarily know how to listen to each other. I often ask them to tell me what someone at their table shared. Working together to solve problems is when the magic really happens. My students seem to be able to do this more frequently and the resulting ideas and reasoning continues to amaze me.

The same is true with really producing music. I found that all of my previous solo experience was great, but the potential for playing with someone made it even better. I enlisted my sons to practice with me. I was that one student in the group that needed a lot of help. Realizing this made me quite sympathetic to the type of student that takes some more time and slows the group down. As we practiced, they supported my need to move the timing down a bit, and gave me tips to help our whole group work together.

---Henry Ford

Working together is the goal of my mathematics classroom. Rich discussion and friendly critique provide an engaging and rigorous classroom. While this is my goal, I have found creating it to be a learning process in and of itself.

First I bring my students together in the classroom by arranging their desks into tables. Listening to each other I liken to keeping together. This I also have to teach. Students don't necessarily know how to listen to each other. I often ask them to tell me what someone at their table shared. Working together to solve problems is when the magic really happens. My students seem to be able to do this more frequently and the resulting ideas and reasoning continues to amaze me.

The same is true with really producing music. I found that all of my previous solo experience was great, but the potential for playing with someone made it even better. I enlisted my sons to practice with me. I was that one student in the group that needed a lot of help. Realizing this made me quite sympathetic to the type of student that takes some more time and slows the group down. As we practiced, they supported my need to move the timing down a bit, and gave me tips to help our whole group work together.

As my 20% project nears the end, I feel I understand the learning process more deeply and definitely have more compassion. Sometimes even though I knew something, it was difficult to perform. Sometimes, I was frustrated when something seemed too difficult (and easy for everyone else.) Sometimes, often actually, I made mistakes. However, ultimately the process was extremely rewarding because of the help, encouragement, and support of my teenage community. I hope that I can offer this to my future students as well.

I have signed up to take a community band class this summer and look forward to maybe one day playing for the USD pep band my sons play in!

]]>I have signed up to take a community band class this summer and look forward to maybe one day playing for the USD pep band my sons play in!

I will often see students nodding along as I, or another student, is presenting at the board. However, when the time comes to explain it, or even work problems themselves, students will sometimes be at a loss over material that they seemingly understood only moments ago.

As I continue to play with Smart Music (online program), I have noticed something. I actually sound much worse when playing with the accompaniment than alone. I credit this to the fact that I can self regulate the difficult parts of a song and slow down my playing to match my ability. It was much more challenging to have the background playing and keeping me accountable. I had to really know and understand how to play the music and wasn’t able to trick my mind into thinking I could play a song.

It is important that we hold students accountable for content. I am not talking about many multiple choice tests that don’t seem to truly check for understanding, but truly authentic assessments. This helps teachers (and more importantly the students themselves) can not trick themselves into thinking something is fully understood. Now, how to do this effectively could very well take my whole career. For now, I will continue to work with my accompaniment to hold me accountable.

Using the internet is wonderful for accessing knowledge. While studying for my CSET math exams I took Calculus from MIT, went through Sal Khan’s videos on Statistics and read up on math history all from my own computer! There are numerous math resources online to help students learn, but you have to know what you are doing in order to find what you are looking for. I am skilled at doing this and know which keywords will produce the content I am desire.

I figured the same must be true with music. After an hour or so, I came up with some pretty good resources. I found an online tuner, a couple of saxophone videos, and a great program called Smart Music.

Smart Music is like a library, class, and coach all at the same time. You can search for any level music for any instrument. The music appears on your screen and you play along. It records you and gives you a percentage and analyzes the notes you missed. More importantly, it simulates playing in a full band which is SIGNIFICANTLY more difficult than playing alone. Many schools use this as homework to help students work on a piece they are playing. You can even submit your score to a teacher.

While Smart Music allows for great practice, it can’t fully take the place of my personal tutors who help me with tone, posture, and dynamics. Technology can’t teach everything in math or music, but it can provide beneficial instruction in each!

Below is a recording of my attempts at Smart Music.

I am feeling pretty good about my new song. I can play most of the notes correctly. I would give myself a 95%, which I consider outstanding, until I really think about it. First off, one wrong note or squeak can really take over a whole song. If I were in a band, one wrong note from each person would result in a pretty poor performance! Also if I ignore the other 5%, the hard part, I won’t know how to do this when it shows up in another song…..and it will.

This happens in math class all the time. We are great with students knowing 95% of the material, teachers, parents, and students all celebrate it. However, take off 5% per year of content knowledge, and we have quite a deficit in math! Just think about the disservice done to students who are passed to the next math class only knowing 60% of the previous classes’ material.

A 60%, or even 90%, pass rate really isn’t acceptable in band. Now, I am not talking about assignment turn in rate, I am referencing the actual performance. The results of such a percentage in band would be dissasterous. I argue that the same is true in math.

Below is a video of an opening speech given by a band director during a concert about striving for perfection and adding personal interpretation.

This happens in math class all the time. We are great with students knowing 95% of the material, teachers, parents, and students all celebrate it. However, take off 5% per year of content knowledge, and we have quite a deficit in math! Just think about the disservice done to students who are passed to the next math class only knowing 60% of the previous classes’ material.

A 60%, or even 90%, pass rate really isn’t acceptable in band. Now, I am not talking about assignment turn in rate, I am referencing the actual performance. The results of such a percentage in band would be dissasterous. I argue that the same is true in math.

Below is a video of an opening speech given by a band director during a concert about striving for perfection and adding personal interpretation.

I am not happy when students do not do their homework. I know how important being consistent with keeping up with assignments is. Without learning the night before, the next day has to be slowed down to compensate. Students will often give excuses as it being too hard or that they were busy.

I really didn’t understand my homework this week. The saxophone piece was too hard, and I didn’t even know one of the notes. I could have asked during the week, but my kids were busy with track practice and by the time they were home from school I was tired. Since it was hard, I wasn’t really motivated to get out my saxaphone and try it on my own. It wasn’t satisfying. It was too hard, and I was busy. My lesson with my sons this week was spent on the same piece as last week and I finally got my questions answered. Next week I will make the effort to move forward and to ask when I need help. Exactly what I expect of my students.

As I consider homework, this is something for me to keep in mind. Students are far less motivated if they are not “ready” for difficult homework. Maybe the concept is one they're are still barely grasping. Or maybe, we only looked at the easy problems in class and the homework requires them to go beyond without any teacher support. Reflecting on this, I remember a talk by Doug Fisher stating that homework should only include review on topics students are comfortable with. I believe that my experience with a difficult song is partially why he recommends this.

Found a great connection with music and math on a site called Math Illuminations.

Music and Math

]]>I really didn’t understand my homework this week. The saxophone piece was too hard, and I didn’t even know one of the notes. I could have asked during the week, but my kids were busy with track practice and by the time they were home from school I was tired. Since it was hard, I wasn’t really motivated to get out my saxaphone and try it on my own. It wasn’t satisfying. It was too hard, and I was busy. My lesson with my sons this week was spent on the same piece as last week and I finally got my questions answered. Next week I will make the effort to move forward and to ask when I need help. Exactly what I expect of my students.

As I consider homework, this is something for me to keep in mind. Students are far less motivated if they are not “ready” for difficult homework. Maybe the concept is one they're are still barely grasping. Or maybe, we only looked at the easy problems in class and the homework requires them to go beyond without any teacher support. Reflecting on this, I remember a talk by Doug Fisher stating that homework should only include review on topics students are comfortable with. I believe that my experience with a difficult song is partially why he recommends this.

Found a great connection with music and math on a site called Math Illuminations.

Music and Math

Moving from a D to a C is hard. In a math class this means being going from showing up and being lucky and on which homework assignments are being graded and which test questions are asked to actually knowing a good portion of the material (70%). I have been finding this transition equally difficult in music. I have a new song, A touch of baroque, that has a measure of slurred notes (that means you don’t stop the note with your tongue before moving to the next one. Instead you allow them to “slur” together.) After practice, I am able to do this pretty well….except from D to C. This is because you go from all your fingers on the saxophone to just one, and change the way you form your mouth (embouchure) all at the same time.

Moving up a grade in math class sometimes just means you need to do one more assignment or be more careful on problems, but often it involves a conceptual leap, especially if assessment is based on understanding and applying the material (as it should be.) Understanding procedure is much different than applying it in both music and math. I often see students heads nodding along as explanations are given. They even say they are totally ready for a test or quiz. However, when they are asked to solve a problem on their own, some of my nodders struggle. The same is true in music. I understand how to play a D and I understand how to play a C. I understand I need to slur theses notes together in a run. I can even express this in writing. However, actually doing it requires more, I have to apply and practice it in different ways. I am definitely struggling and at times frustrated (as anyone trying to learn something new might be.) While it helps to get tips, this is going to be one of the leaps I need to make before I can play this piece.

Moving up a grade in math class sometimes just means you need to do one more assignment or be more careful on problems, but often it involves a conceptual leap, especially if assessment is based on understanding and applying the material (as it should be.) Understanding procedure is much different than applying it in both music and math. I often see students heads nodding along as explanations are given. They even say they are totally ready for a test or quiz. However, when they are asked to solve a problem on their own, some of my nodders struggle. The same is true in music. I understand how to play a D and I understand how to play a C. I understand I need to slur theses notes together in a run. I can even express this in writing. However, actually doing it requires more, I have to apply and practice it in different ways. I am definitely struggling and at times frustrated (as anyone trying to learn something new might be.) While it helps to get tips, this is going to be one of the leaps I need to make before I can play this piece.

Just as I thought my counting was getting pretty good, I was introduced to fractions. This happens to my Algebra students all the time, and even some of my Calculus students. I would say students make more mistakes with fractions than any other concept in higher math classes. Divide a fraction by a fraction and the whole train has to stop. Add a variable to a fraction, and it is like the fraction suddenly becomes an entirely new concept. In the past this used to be a source of frustration for me. After all, these students are in high school Why don’t they know how to work with fractions?

Turns out the same is true in music. It is taking counting to a whole new level! I have learned that there are 8th and 16th notes (and rumors that there are even dotted 8th notes where you take 1/8 +1/16.) Not only that, but 3/4 time means that there are 3 beats per measure, but the quarter note has one beat. My own kids assure me that this will become automatic, especially the “easy” ones like 3/4. It is definitely not easy for me yet.

Even though I feel like I am very strong with fractions, applying them while playing is a whole new level! I definitely can not put all of the knowledge about the way this works into practice yet; it is an entirely new concept. I am understanding my students more every day while improving my music knowledge.

Here I am trying to play while encountering very simple fractions.

Turns out the same is true in music. It is taking counting to a whole new level! I have learned that there are 8th and 16th notes (and rumors that there are even dotted 8th notes where you take 1/8 +1/16.) Not only that, but 3/4 time means that there are 3 beats per measure, but the quarter note has one beat. My own kids assure me that this will become automatic, especially the “easy” ones like 3/4. It is definitely not easy for me yet.

Even though I feel like I am very strong with fractions, applying them while playing is a whole new level! I definitely can not put all of the knowledge about the way this works into practice yet; it is an entirely new concept. I am understanding my students more every day while improving my music knowledge.

Here I am trying to play while encountering very simple fractions.

I still have one of my kids counting for me through the songs, but am trying to become more independent by tapping my foot. I just really wish my foot could count out loud.

]]>One task you simply must know in Algebra is how to graph a line. I find this very basic since everyone has experience with lines and slopes. This is considered a beginning entry point to variables in Algebra. I have probably graphed thousands of lines in my life. This started back in pre-algebra when I used two points and a t-chart and continued all the way up through Calculus graphing a tangent line. I would definitely call myself an expert on graphing lines. I know several ways to graph lines, that lines represents infinite solutions, and that lines divide the coordinate plane in half. Rarely do I express these when graphing, but they are always in the background. I can see an equation of a line and know what it is going to look like by noticing the slope and y intercept or thinking about the two solutions. For me this is automatic. It is as easy as counting to four, ...or is it?

It turns out in music counting to four is entirely different that how I previously understood counting to four. Sometimes you count to four quickly, sometimes slowly. They have fancy words that tell how to count like*Vivace* and *Largo*, but for now I am just trying to get counting to four at medium speed down (however, there are several medium speeds.) Not only do you have to count to four at the same pace through the entire song, but you have to remember where to put your fingers, how to make an embouchure (the way you form your mouth to actually make a sound), and read what note you are supposed to play.

The really tricky part comes in when you don’t actually play a new note for each of those counts. When playing a half note you are counting to two twice and four simultaneously. You can’t even count out loud because you are desperately trying to make this embouchure so you don’t squeak while reading, fingering, and playing the note. It is exhausting and very overwhelming. This doesn’t even tackle the “rests” which are not restful at all, because you are still counting to four and trying to look ahead for the next note.

Luckily, after several failed counting and playing attempts, my son broke it down for me and had me clap the melody several times and counted out loud while I played. He tried introducing me to an online metronome (a clicking music counter), but I got lost. There is also this page at the back of my music book called rhythms that he assigned for this week. It looks pretty boring (as I am sure a page full of graphing looks to my students). However, after trying to go too fast and failing, I know I need more practice. I thought I would be able to play a real song by the end of this week to play, but I am still working on counting to four with nursery rhyme tunes.

I hear rumors that sometimes you don’t even count to four, you count to two or three. However I liken this to parabolas and cubic equations and consider it advanced and for later learning.

]]>It turns out in music counting to four is entirely different that how I previously understood counting to four. Sometimes you count to four quickly, sometimes slowly. They have fancy words that tell how to count like

The really tricky part comes in when you don’t actually play a new note for each of those counts. When playing a half note you are counting to two twice and four simultaneously. You can’t even count out loud because you are desperately trying to make this embouchure so you don’t squeak while reading, fingering, and playing the note. It is exhausting and very overwhelming. This doesn’t even tackle the “rests” which are not restful at all, because you are still counting to four and trying to look ahead for the next note.

Luckily, after several failed counting and playing attempts, my son broke it down for me and had me clap the melody several times and counted out loud while I played. He tried introducing me to an online metronome (a clicking music counter), but I got lost. There is also this page at the back of my music book called rhythms that he assigned for this week. It looks pretty boring (as I am sure a page full of graphing looks to my students). However, after trying to go too fast and failing, I know I need more practice. I thought I would be able to play a real song by the end of this week to play, but I am still working on counting to four with nursery rhyme tunes.

I hear rumors that sometimes you don’t even count to four, you count to two or three. However I liken this to parabolas and cubic equations and consider it advanced and for later learning.

One of the things that bothers me most when I talk with people about my chosen profession, math teacher, are the immediate responses.

"Oh wow! I don't have a math brain."

"You are so lucky, I just don't have the math gene."

"I just am not mathematical."

Somehow it is okay to say these things in our society. No one would ever say, " I just never learned to read." or "I don't have the reading gene." They may say they don't like to read, but that is entirely different that saying they are unable to learn to read.

I believe that any person can learn and become mathematical. I don't believe this is easy. It requires trial and error, persistence, consistency, mentoring, and being willing to learn from mistakes.

I am not musical. I can't really stay in tune when I sing, I don't play any instruments. All three of my children excel in music. They understand it in a way I can't comprehend. Moreover, sometimes I can't even follow their conversation due to the high level musical vocabulary. I joke with people that I don't know where their musical mind came from; they certainly didn't get their music genes from me. I feel like they are so lucky to be able to enjoy this music brain they seem to have.

I just realized that I am a complete hypocrite!

Somehow it is not okay when people say such things about math, but music, that is another story. So it is here I apologize to the many people I have told that I have no musical talent, and I don't know where my children got the music "gene" from. I also apologize to my children, who have worked hard to become musical through trial and error, mentoring, persistence, and consistency. I don't have a musical brain......yet.

I am beginning my journey today with learning to play the saxophone. It is one of the "extra" instruments we have around our house. My sons assure me that this is the easiest instrument to learn to play because the keys are in order. I don't quite understand what that exactly means, but "easiest" sounds less intimidating. I imagine that is why the math problems in a book go from easy to more difficult. First on the agenda....putting the saxophone together!

]]>"Oh wow! I don't have a math brain."

"You are so lucky, I just don't have the math gene."

"I just am not mathematical."

Somehow it is okay to say these things in our society. No one would ever say, " I just never learned to read." or "I don't have the reading gene." They may say they don't like to read, but that is entirely different that saying they are unable to learn to read.

I believe that any person can learn and become mathematical. I don't believe this is easy. It requires trial and error, persistence, consistency, mentoring, and being willing to learn from mistakes.

I am not musical. I can't really stay in tune when I sing, I don't play any instruments. All three of my children excel in music. They understand it in a way I can't comprehend. Moreover, sometimes I can't even follow their conversation due to the high level musical vocabulary. I joke with people that I don't know where their musical mind came from; they certainly didn't get their music genes from me. I feel like they are so lucky to be able to enjoy this music brain they seem to have.

I just realized that I am a complete hypocrite!

Somehow it is not okay when people say such things about math, but music, that is another story. So it is here I apologize to the many people I have told that I have no musical talent, and I don't know where my children got the music "gene" from. I also apologize to my children, who have worked hard to become musical through trial and error, mentoring, persistence, and consistency. I don't have a musical brain......yet.

I am beginning my journey today with learning to play the saxophone. It is one of the "extra" instruments we have around our house. My sons assure me that this is the easiest instrument to learn to play because the keys are in order. I don't quite understand what that exactly means, but "easiest" sounds less intimidating. I imagine that is why the math problems in a book go from easy to more difficult. First on the agenda....putting the saxophone together!