Math Like Jazz

     There is a lot of hoopla out there about common core and for the most part, I ignore what people have to say. I doubt that most people who write something on Facebook for or against common core have actually analyzed the standards or the reasoning behind any of them. Now, I am no expert, but I have been to hours of training, I've studied the standards for math, and I am on the pilot team for common core math at work. I thought I might write a little bit about common core so that those of you who care can get some inside information.

      First of all, I am not a piano player. Anyone who actually plays piano would testify to this. I know how to play piano just like I play every other instrument I play - just enough to know how little I actually know. I love the piano and I wanted to learn how to play. I had two goals: I wanted to play the first movement of Beethoven's "Moonlight Sonata" and I wanted to be able play jazz style piano. I already knew how to read music and which notes corresponded to which keys on the piano. I practiced the first movement of moonlight sonata like crazy. I played it every day. I had a piano teacher critique it and help me through the parts I didn't understand. I listened to it over an over again. Now, I can play the first movement. I can play it well enough to convince someone that I might actually be able to play a little. 

    So the first task was complete, on to Jazz. I had a lesson with a really great jazz piano player I know. I sat down with him and he had me play a C chord, which I did...and that was the first and last part of the lesson I actually understood. He went on to talk about circles of fifths and how one scale can be changed to another and transposing and all sorts of things that were so natural to him and he assumed would be natural to me. So I postponed my jazz instruction because I now know what it takes to play jazz. I know that if I want to riff and run as if I'm playing from my heart, I have to have the strongest of foundations in music theory and piano practice. 

     I can't yet play jazz, but I can play math. Math is not some mystery to me, it is not magic. It is an interaction of numbers that have distinct relationships with each other. The relationships between numbers are well known to me. I know them like I know the relationships between characters on "Gilmore Girls". For example, if you asked me, "What is 30 - 12?" I might simplify it in many different ways. I could write the numbers on top of each other and subtract by borrowing. I might also see the 2 becomes 10 by adding 8 and 8 and 12 make 20 and 20 and 10 make 30 so 8 and 10 are 18. I might also picture a number line and break that number line up into jumps of 5's and see that 12 needs 3 to be 15 and 15 needs 15 more to be 30 so 3 and 15 are 18. You may think that these other methods are time consuming and tedious, but they actually make it tons easier for me to do subtraction in my head. While others need to write down 30-12 and then cross out the 3, make it a 2 and add a 1 next to the 0 and then start subtracting, I would much rather add my way to 30. I find that I actually add to solve most of my subtraction problems. 

      Here's the deal. It doesn't matter which way you get the answer as long as it's right, but because I know the ins and outs of number relationships, I am able to choose the path that works the best for me. I get the numbers. I know what I'm doing no matter what method I'm using. I play math like a jazz musician, letting my heart express itself freely because I have the foundations of understanding how the mathematical musical structure works. 

       We are a  society that loves shortcuts. We want the fastest solutions, the shortest way. We want to know the answer. We are an answer driven educational society as opposed to a process driven society. We learn algorithms (a set of steps that lead to a solution) without knowing anything about why we are doing it. Some of you may remember how to change a mixed number into an improper fraction. Some of you may just barely remember what those words mean. Most of you have no idea why you multiply the denominator with the whole number, add that product with the numerator and then write a new fraction with that sum over the same denominator. And because most of  you don't know why you do that, most people forget some or all of the steps or mix them up or have a vague sense of familiarity with that process and think, "Can't I just make them all decimals and let my calculator do it?" My answer is, "No." Asking a math teacher that question is like saying to a literature professor, "Can't I just watch the movie instead of reading the book?" Memorizing algorithms is actually really hard. Memorizing algorithms when you don't even know why you are doing it is like trying to memorize the words to poem you don't understand in a language you don't speak. It's incredibly difficult to do.

       We have taught our students the shortcuts but not the math. They have little to no number sense. About half of my students last year, when given the problem of 15.25 - 1 actually would consistently get 15.24 and not 14.25 because they followed the subtraction algorithm: write the numbers on top of each other and subtract. There wasn't a picture in their heads about how much 15.25 is and how much 1 is. There was no connection to money or measurements or any other practical application. There was an incorrect application of the algorithm. Because the algorithm meant nothing to them, they had no concept of whether their answers were right or wrong.

        Common Core math is an effort to force our students to take the long way. To force them to see and explain why they are doing something. This means that students will often be expected to write out a long procedure that we, as well trained adults, know a super quick shortcut for. That shortcut will eventually be taught and the students will add that to a set of tools they have a firmer understanding of, but in the meantime, they need to learn the why's and how's. It is painful to teach a child that in order to add 5 and 6 they need to draw a number line and draw 5 jumps of 1 and then 6 jumps of 1 and then count the jumps and find that it is 11. But the reward is that when I ask the same child to add 5 and -6, he or she can draw 5 jumps of 1 in the positive direction, jump 6 jumps backwards and land at -1 and really trust that that is the answer without trying to remember which rule it is. Trust me. I have taught the lowest performing students in my school using a similar method for the past 5 or so years and it is amazing what they can do. They know what 3/4 looks like and can compare it to other numbers. They can add numbers with decimals and not mix up place value. It is the long way, but it is the way that will keep math understanding in our students' minds.

        Common Core math is not perfect, neither are the books that present it, nor the teachers that teach it. It takes a lot to train yourself as a teacher to let your students struggle. It is new to us too and we will fail frequently as we attempt new methods of teaching, assessing, grading, and learning. If you have a child in the public school system, you will probably be frustrated frequently with many aspects of the new standards being taught. But here's the thing: If I don't take the time to learn the why, I'll never be able to play jazz and in the long run this is the path that will get us there. 

Waiting

   Last Spring I went to and spoke at a women's conference where the topic was "Trust in the Lord" and before and after that weekend I keep learning about how important that lesson really is. I spoke about how we need to trust God when our hope is deferred. For the past few weeks, I've been taking care of my sick husband. He is not going to die from his illness and he will recover in due time. However, he's been racked with pain, fever, chills, swelling, and the inability to eat even though he's hungry. I've watched him progress from one horrible symptom to a day of getting better and then on to the next horrible symptom. Each day is filled with prayer to God - thanking, praising, and pleading. Each day, we are told to wait for healing.

      I read this morning in Ephesians chapter 3 and when I read the end about how God is able to do immeasurably more than we ask or imagine, I went through this thought process:

1) So what's he waiting for?

2) Why isn't he healing Nathan completely and instantly? He could do it!

3) Maybe he's teaching us in this waiting period. Maybe the "immeasurably more" part means he can do more than just heal Nathan by not healing him. So what could that be? What is the immeasurably more part that God is doing? I can't ever really know because God's wisdom is definitely beyond mine and the tapestry he weaves is only revealed in part to me. But I have some ideas...

    I am learning that my husband's character at his core is just what I thought it was when he was well. He is just as kind, just as patient, just as ever selfless and concerned for me as he ever was...maybe even more so. 

   Nathan is learning that I am bossy and a bulldog when it comes to protecting the ones I love. He's learning that he can depend on me to be by his side.

    We are remembering the blessings of begin married. We don't have to do this alone. I can fill out his medical forms while he waits in the waiting room. I can keep track of which meds he's taken when and how soon to his next dose so his tired mind doesn't have to remember. We have larger families and a bigger circle of friends now that lift us up in prayer, bring us food, clean our kitchen, and listen when we need them to.

   Just before all of this, we were having a discussion about God and healing and why he sometimes does and sometimes doesn't and then we started to experience this first hand. I think God is teaching us to rely on him even when we don't get instant healing. We talked about how as teachers, if we just gave our students the answers without letting them struggle, they wouldn't learn as well as when we let them grapple and think. We as teachers are always watching over them and guiding them, but we don't just give the answers immediately. We let them struggle and watch them grow. We thought that maybe this was how God is with us. In our struggles, we learn and grow. God is not distant in these times, he is carefully watching every step, every struggle, tenderly caring that it hurts and feeling our sorrow and pain, but also aware that in this pain we are growing and he can joyfully see the ending and the purpose. He tells us that it will all work out for good. He is in this, even in the pain, he is here with us able to heal, but able to do immeasurably more than that too.

Watching Love Grow

For those of you who know me, I love love. I also love the idea of being married. As a five year old, when asked what I wanted to be, I responded, "A wife and a mother." This was not because of some ingrained lesson my parents taught me about a woman's place or anything. I was given plenty of options for a future career and I did not feel limited as to what I could do. I think it was because my mom was (and is) my hero and greatest role model and she was a wife and mother - what better job could I find? In fact, this same woman asked me as I headed off to kindergarten, why I was excited to start school like my brothers before me. I answered, "I need to go to school to find a husband!"

    So fastforward nearly 30 years later. Thirty years of wishing and dreaming. Thirty years of filling my head with RomComs, Jane Austen, Shakespeare, poetry, and CCRNs (cheesy Christian romance novels). In that time I was careful not to be unrealistic about what marriage was. It wasn't going to be some endless hallmark movie. It wasn't going to be life filled with candlelit dinners and witty repartee (although that could be a part of it). It was going to be filled with normal things and difficult things and the messy parts of life too.

    Then I met Nathan. I loved Nathan more and more as we dated. Eventually it actually hurt for me to say goodbye to him when we were done with a date. He would drop me off at my place and I would cry for a bit and text him immediately and then ask him to call me when he got home and we would talk for another hour until I couldn't stay awake. Wow, that sounds kind of pathetic, but it's actually sweet, trust me. I just loved him so much, I couldn't bear to be away from him. As our wedding neared, I started counting down the goodbyes. "Only thirty more goodbyes and then no more forever."

    So, after all that anticipation, all that dreaming, all that planning and wishing, how do I feel? I feel like all of my dreams and hopes were not even close to how wonderful it would be to be married to the right man. Every day I feel like I love him more. Every day I think, "I'm really married! He's mine forever!" Every day I know that I don't have to say goodbye. Every day I praise God for this gift.
  
   Now school is starting and we will have less time to spend with each other and we'll be apart more and I'll start texting him again, but the best part is that we don't have to try to figure out when we'll see each other next or what place is open for us to hang out past 10 pm. I'll come home to Nathan and he'll come home to me. I feel overwhelmed by love. Who knew I could love him more? But I do, every day. Who knew marriage could be this awesome? Lot's of people, I'm sure, but I'm glad that I get to experience it. I know that there will be difficult times to come, but I also know that Nathan is my faithful friend, devoted husband and that that will never change.

Perfect

    I always had certain ideas of what an ideal proposal would look like: the guy on one knee, no jumbo trons, a quiet place, a beautiful ring and a sweet speech. Nathan only knew that I wanted my dad to be asked and that I didn't want some huge public scene. We had kind of talked around the idea of getting engaged without really saying it out loud. "Someday I would want someone to do this..." or he would ask me what I liked in jewelry and I wasn't sure if he meant jewelry or jewelry.
    Nathan and I started talking about spending Valentine's together and how Friday the 15th would be better for us so we wouldn't have work the next day. I had no suspicions as the day neared until almost two weeks before. Nathan started saying things and being just a little different. I wasn't allowed to look at his phone. He would look at me differently or say things differently and suddenly, I just knew. I wanted to keep it a surprise and not ruin it, but I made sure that my nails looked nice and my makeup was camera ready.
     When Friday rolled around, Nathan showed up at 4 to pick me up. He opened the car door revealing a single red rose on the seat of the car waiting for me. I love flowers and this was so beautiful - a perfect start. As we started driving I found myself getting really nervous. I was excited about the possibility of him asking me and then anxious to think, what if he didn't! Nathan seemed as calm as could be, which only added to my nervousness. He seemed too calm...
      The car arrived at Laguna, a beach where we had had a previous date early on in our dating that can only be described as strangely beautiful. It involved a harpist, several strangers photographing us several different times and at several different locations, and several other groups of people talking to us about love. It was memorable, to say the least. Once we found a parking spot, Nathan pulled out a picnic basket, blanket, and backpack. I had a gift for him and my rose. I wondered where he might have put the ring, but he seemed pretty free about me seeing any of the bags or baskets, so I started to doubt again - had I scrubbed my hands and filed my nails for nothing?
      We walked along the boardwalk toward the sand and settled near the base of the cliffs with the sunset over Nathan's shoulder and a view of cliff-front homes over mine. The wind, which had been roaring all day, stopped and the temperature was in the 70's - a perfect beach day! He set up an amazing spread with a red tray, votive candles, gourmet food he prepared, my favorite cheese, pomegranate seeds, and lots of water (my beverage of choice). After he set up the meal and we prayed over it, I saw him sitting across from me, smiling and calm as could be. I started to doubt if this was the night. I couldn't think of anything to say, so I had him open his present from me (a book filled with pictures of our dates and texts we had sent to each other) and he looked at each page, admiring all of my efforts and responding exactly as I had hoped he would respond.
      I could barely eat, I was so nervous. "When's he going to do it? What's he going to say? What if he doesn't ask me and I feel foolish for being so sure?" As the sun set, the beach suddenly emptied. It was strange, the sky was still a beautiful orange and the sunset was not quite done and a mass exodus of people started. Nathan asked me to stand next to him to watch the final rays flash above the horizon and there we were, alone on the beach.
    He looked down at me and I looked up at him and he said, "I want to spend the rest of my life with you." "I want that too," I barely said while thinking, "this is it!! Memorize every moment!"
    Then he said, "I have your father's blessing," and I started crying. He smiled and said, "I guess there's just one thing left to do," and he got down on one knee, pulled out the ring and said, "Will you marry me?"
    I was sobbing and threw my arms around him and kissed him and then realized I hadn't said anything, "Yes, yes, yes!" and then I hugged him again. He gave me the ring (which was exactly what I want in a ring), opened up a bottle of champagne and brought out a dessert of banana and strawberry slices covered in Godiva chocolate. We spent the next hour and a half just savoring the moment and trying to let the reality of it wash over us: I am going to be Mrs. Landmon! We would grow old together! We were going to plan a wedding! The stars were so bright and the homes on the cliff twinkled with lights. We walked back to the car and one of the restaurants was playing American Standards from the 50's (our favorite music) and Etta James "At Last" started playing. Could any song better match my feelings at that moment?  "At last my love has come along..." and he has.

One Step Closer To Being Sydney Bristo

    To get a full grasp on this story, I must start with a lesson I teach to my students every year about slope. I start by asking my students where they've heard slope before and oftentimes they will respond, "mountains" or "skiing" and that's when I start to tell my stories about how much I hate snow sports. I talk about how I've gone skiing or snowboarding and ended the day broken, crying, cold, and miserable. I tell about how I fell into a gully and had to be rescued, how I fell flat on my face and literally knocked the snot out of me. I tell how it is one of my least favorite things to do.
    Also, to understand this story, you must know that my boyfriend loves skiing. It is his favorite sport. He lived in states with excellent skiing: California, Oregon, Utah. He dreamed of being able to take me skiing with him to share in one of his favorite activities.
   You can imagine how we both felt about the situation. Yet I realized that in all relationships, one must learn to compromise. I had months to prepare myself, to tell myself that I could do it, to convince myself that the fun clothes and promised hot chocolate would be worth it, and that if it made my boyfriend happy, it would make me happy. Months to prepare for the day when enough snow had fallen and winter sports had come.
    Yesterday, the day finally came. I was prepped in my cute clothes and brought a great picnic lunch along and suddenly, I found myself in line for my first ski lift in probably 14 years. The bunny slopes went great. My boy was a great teacher, giving me just enough tips and instructions to be helpful and improve my control of the skis without being too helpful or annoying. I fell twice the first run, but after four trips up, I was ready to move on - beginner runs for me!
     We rode to the top of the beginner run and I was suddenly filled with fear. I'm not afraid of much. I kill spiders and talk to homeless people and speak in front of hundreds at a time and it's no problem for me. I've swum with sharks, jumped of balconies on homemade ziplines, and taken 40 jr. highers to Catalina on a boat. But I was overwhelmed by the fear of falling off the course, falling in the path of other equally bad skiers, getting run down by people, speeding out of control and rolling head over heels until I break something. I knew I needed to calm myself down and gather my courage, so I suggested we look through the lodge at the top of the slope.
     That didn't take as much time as I wanted, but off we went. It actually wasn't too bad. I made it safely down and started to see that I wasn't so horrible. Maybe I could do it again - so I did. I was gaining confidence and feeling like I could get past my fears and actually even get better at this whole skiing thing.
    We decided to try a different beginner run. This run started in the same place as a blue square run (an intermediate run that also had a freestyle section filled with jumps and ramps and rails) but soon after, the runs diverged and we could follow the easy run down. We started down slowly and soon found the signs for the green beginner run - only to find that it was closed! We flagged down a ski patrolman on his snow mobile and asked what we could do. "Take the intermediate run down, I guess." I could feel the tears starting to form and my chest tighten. I eyed the back of his snow mobile - it could easily seat two people. I stared at him with a look that pleaded for him to offer me a ride to the top. I considered just getting on the back without an invitation when he said, "good luck!" and drove off.
    "Ok, babe, you can do it," I heard as I started to tremble. Wonder woman wouldn't cry, but I wasn't feeling much like her today. I just looked ahead at the ramp with snowboarders flying off and then what seemed to be a sheer cliff melting into the skyline. With a few more instructions and some practicing of my stopping techniques, we started down the mountain.
   I ran into one snowboarder, causing us both to fall, but he was so awesome and helped me back up. I fell several other times (a surefire way to stop when I felt like I was going to die), but mostly just slowly went back and forth one piece at a time. The snow was actually more powdery on this less used run and because everyone else was so much better, I didn't really have to be afraid of someone running into me. All I had to do was stand still and let them work around me.
   What was most amazing was my boyfriend. He was so patient and so encouraging. He would ski ahead a bit when the drop would get too steep to see, and let me know which path would be the easiest. He calmed me down and helped me take it one little piece at a time. He helped me navigate away from all of the scary trick parts of the run and told me when the coast was clear so I could start my way down. And even though I was terrified, I actually felt really good knowing how awesome he was to me.
      I about cried with relief when I saw the final steep slope that would lead me to the lodge at the bottom. It only took me an hour to do a run that most people probably finish in thirty minutes, but I had done it and survived.
    I spent the next hour sipping hot chocolate in the lodge by the fire, waiting for my boy as he fit in a few runs without me. I was definitely done for the day, but I was also proud of myself. I faced a fear and finished without peeing my pants or fainting or even being too weepy. I was proud of my boyfriend too. He was an unbelievable helper and literally talked me off a cliff - or at least down one.
  So I may not be wonder woman nor Sydney Bristo, but I feel like I am one step closer. So if I ever find myself chasing a bad guy down a mountain slope on skis, I feel like I won't be helpless - I just better hope and pray that the bad guy goes really slowly.

Oh, Man, I Am a Nerd!

  I admit to being a nerd. I understand and embrace many nerdy things. I have no shame in this because I feel like I balance that nerdiness with good social skills. I can interact with people about all sorts of things that don't involve time travel or fantastical landscapes. But as I stepped back from my conversation with my friends at dinner last night, I realized just how nerdy we all are. Here are some snippets of things my friends and I said:

1) Rick Riordin's next series is coming out and this time it's all about NORSE MYTHOLOGY! I'm so excited!
2) So let's prioritize the rest of our comic con schedule. If you had to choose between the Hobbit panel and Merlin, which would you choose?
3) Oh, man, I messed up my Mobius strip scarf!
4) Oh, I see, I needed to twist it 360 degrees not 180 degrees. Because a 360 degree rotation in the round is like a 180 rotation with paper!
5) All of my favorite YouTubers are just down the street in Anaheim and I can't go see them!
6) You have Lois Lane hair!
7) Which Lois Lane?
8) The best one, Teri Hatcher!
9) Did you get me a VanGogh exploding Tardis Dr. Who shirt for my birthday? Awesome!
10) What'd you get Cathy, a GMAT study book? Oh, you did!
11) Let's practice the math section!
12) I think I need to knit Adam Baldwin a scarf to match the cunning hat and give it to him at the Firefly panel!
13) I'm sure the Dr. Who panel will be on Sunday and the Hobbit will probably be on Saturday, so there are no conflicts.
14) And then the Simon and Schuster panel is that night and I think they might be giving away free SWAG - like maybe even new books!!
15) That would be a good shirt to wear to comic con, except it's not nerdy enough.
16) I have to pick out what books I'm going to bring to comic con...maybe I'll get some e-books from the library to reduce the weight I'm carrying.

So we were at a comic con planning party, which increases the probability of nerdy comments being said, but I am a nerd. I was rooted in nerdiness as a child and that nerdiness was allowed to grow slowly and quietly until it bloomed and became complete in me. I am a nerd.

Frustrated Poetry

        I was at a really difficult meeting today that I struggled with. During one portion of the meeting (when my blood sugar was at its lowest) I was staring at the floor which led me to stare at the pant leg of the guy sitting next to me and noticed that he had a paperclip at the bottom hem of his pants. Why? It wasn't holding the hem together, it wasn't doing anything. I was transfixed by this paperclip and started saying in my head, "paperclip, paperclip, paperclips" and then "clipper ships, clipper ships, clipper ships" and then I wrote a poem:

                       Paper clips and clipper ships
                       floating in my head

       This is a sign of bad things ahead. I know that when I feel the poetry start to flow, the meeting has been too long and I need to step outside, call my mommy, or get some food.

    Later, after lunch, a man in my group was talking and talking and I couldn't make my brain listen to him. I tried to take in what he was saying and repeat it back in my head, but I just couldn't do it. All I could think about was how slow the time was going and how I really wanted to be done and how torturous this was beginning to feel.

                            slow, tortured time ticking by

      I don't do well at 7 hour meetings, no matter how well planned they may be. I cannot be expected to sit still for that long! No one as hyper as I am should be expected to sit that long...I have such sympathy for my students! Wow, I seriously just considered that this must be what school is like for so many of my students. Maybe I should start wearing paperclips on my pants to at least inspire some poetry.