30 Day Photo Challenge: Day 5 Nature

Canna Lily

Canna Lily

“Mathematics is the language of nature.” ~Galileo

This is a picture of a canna lily leaf in my backyard.  They are hearty plants and are easy to grow. In fact they multiply over the years so you can dig up the bulbs, separate them, and replant them elsewhere in the garden.  This beautiful spiral caught my eye as well as the striking patterns and colors on the broad, green leaves.  Fibonacci spirals are found in many places in nature. Think seashells and the spiral shape of the galaxy.  Fibonacci spirals are formed following the Fibonacci sequence, where each number is the sum of the two preceding numbers.  Fibonacci numbers like 3, 5, 8 can be seen in flower petals, tree branches, and spirals found on pineapples, pine cones and other natural phenomena.  Have you ever noticed that before?  It’s super cool.  Math is everywhere!

Check out some of these examples:

Disk florets of yellow chamomile (Anthemis tin...

Disk florets of yellow chamomile (Anthemis tinctoria) with spirals indicating the arrangement drawn in. (Photo credit: Wikipedia)


Aloe polyphylla

Aloe polyphylla (Photo credit: Wikipedia)

English: Fibonacci Spiral generated with the f...

English: Fibonacci Spiral generated with the free software GeoGebra (Photo credit: Wikipedia)

A tiling with squares whose sides are successi...

A tiling with squares whose sides are successive Fibonacci numbers in length (Photo credit: Wikipedia)


Thanks for reading this entry. Peace out!




Pearls on a String: One year later.

One year ago today, I quit my teaching job. Why? I wrote about in this entry: Pearls on a String. Since then, I’ve been adding pearls to my string of wisdom and experience. I’m a numbers person, and I can’t help but remember the day that my life changed unexpectedly, March 9, 2012, the Friday before Spring Break.

Today, my oldest daughter (19) is on spring break from college and enjoying her first vacation (Destin, FL) without her family and just with her friends. My two school aged kids (12 and 8) started their spring break yesterday too. My stepson (20) is an infantryman in the U.S. Army stationed in New York.

English: Beach in Destin, FL

English: Beach in Destin, FL (Photo credit: Wikipedia)

Last month, I renewed my Texas teaching license (Generalist 4-8), and last week, I passed the licensure test for Math 8-12. I tutor privately at home and on Skype and am a full-time mother.

Math Dances

Math Dances (Photo credit: Dylan231)


A year ago, my daughter (12) was coming home alone after school until about 6:30 when I picked up my son (8) from after-school care. There was no after-school care for her; sixth grade is the fist year of middle school here in Texas. Now, I am available for both of them after school, and I’m able to provide transportation for her to take dance classes sixteen hours a week. She’s grown tremendously in all aspects over the past year. She’s keeping up her grades at school, and she’s grown by leaps and bounds in her dance skills (pun intended). My son is also thriving at school and in his sports: taekwondo and baseball. My stepson (20) was able to visit us last March, and we saw him at Christmas. I was able to visit my oldest daughter (19) for ZTA mom’s weekend last month.

I’m able to set my tutoring schedule around our family schedule and am able to spend time pursuing other interests like guitar lessons and blogging. My husband made partner at his law firm in the past year. At first, I was devastated, but I can honestly say I am truly grateful for the opportunity that fell in my lap. I miss the kids, but I still get to work with wonderful students. And most importantly, I’m able to put my family first.


Daily Prompt: Time Capsule 2012

“The year is drawing to a close. What would you put in a 2012 time capsule?”

1.  A dance bag with ballet, jazz and hip hop shoes and gear. This is the year my daughter (12) became super serious about dance, and our lives now revolve around her practice schedule.

2.  An iphone.  Four out of five of us in the family have iphones. They are definitely a sign of the times.  They have itunes libraries reflecting today’s music too.

3.  My Obama victory magnet.  It’s on the back of my car. I’m happy that he won reelection this year!

5.  Camoflauge pants and combat boots to represent my stepson (20) who is now in the army, stationed at Ft. Drum NY.  He is an infantry man. We are super proud of him for his sacrifice and service.

6.  A Texas Tech flag and a Zeta Tau Alpha sign to represent our daughter (19) who is a ZTA at Texas Tech. She loves going to school there!

7.  My son’s (8) last baby tooth in the front that finally fell out (the yellow one).  It was yellow because when he was a toddler he fell down the stairs and whacked his face and mouth on the tile floor. It cut off blood supply to his tooth, so it turned yellow.

8.  My husband’s business card. This is the year he made partner at his law firm.  He also turned 40 this year (officially over the hill).

9.  An Algebra 2 book because I’ve been studying it a lot this year.  I’m a private math tutor, and I have kids everywhere from Pre-Algebra to Algebra 2 and in between.  This year, I have lots of kids in Algebra 2 and have been enjoying working with them.

10.  An electric guitar because this is the year I’ve been taking lessons consistently and finally learning more about music theory and writing solos.

My Love Affair with Math

I started preschool when I was two years old then skipped kindergarten starting first grade at five years old. I don’t remember much of that early learning, but I do remember puzzles and playing music. My mom is a musician, and she started me on violin (Suzuki method) at the age of three. I grew up knowing how to read music on the violin, and I think that might have been an important step in my brain’s development that led to my understanding of math and science (thanks mom). Music is all math and science.


I do remember doing math in the early elementary years, and it was always easy. I had good number sense. The first few years of elementary school were a breeze, and the only thing I got in trouble for was singing or humming in class. I understood place value and basic computation. I learned multiplication and division with no problem. After third grade, my mom decided I should repeat third grade so I could be with my age group, and I did fourth grade work. I scored in the genius category on IQ tests and took GT classes through elementary and middle school. Again, I don’t remember much about those years, or particularly liking math at that time, but I do remember it being easy. My mom called me a walking telephone book because I could always remember phone numbers with ease (the same is true for today except that with iPhones I do admit I don’t know everyone’s phone numbers like the old days in the 1970s-80s). But I’ve always had a good memory for numbers and patterns.

Looking back at my high school transcript (Class of 1986 Go Lancers!) I can see why my guidance counselor advised me to pursue a major in French and then return to the Washington, DC area to work at the state department as a translator. I took four years of French and got two B+s and two As. Only three years of math were required back then, so I only did the bare minimum. I got a B in Algebra 1 (ninth grade), a B in Geometry (tenth grade), and a C in Algebra 2/Trigonometry (eleventh grade). Everything got confusing once we got to logarithms. I don’t remember having hatred or dislike toward math, but I don’t remember particularly liking it either. My m.o. back then was to do ok academically and still have a social life and a love life. I did gymnastics and cheerleading and played soccer. I talked a lot in class and was a social butterfly even back then. I had no idea what I wanted to be when I grew up, so I took my counselor’s advice and started my freshman year at Hollins College as a French major. Nobody made me take a math class that year. I did take computer science and programming, which is mathematical, but there was no other math requirement that year. My sophomore year, I did an exchange program at Washington & Lee University. There, I switched my major to Philosophy & Religion. I took a music appreciation class, but again, no math class. I took my junior year off and worked for Greenpeace USA in DC then completed a Spring Semester in the Rockies with the National Outdoor Leadership School (NOLS). After that, I transferred to Prescott College and changed my major again to Environmental Studies. I minored in Outdoor Education and Liberal Arts. I passed the math proficiency test there and didn’t have to take any math classes (the proficiency test is equivalent to college algebra).


I graduated from Marymount University with my master’s degree in education (M.Ed. PreK-8) and became a teacher. My first position was sixth grade, all subjects in Reno, Nevada. Sixth grade deals with a lot of fractions and decimals, yet many of the students were below grade level and still working on memorizing multiplication and division tables. That is when I first started to take an interest in math education. It was a challenge to teach sixth grade skills when kids lacked knowledge they should know from previous years.  I moved to Virginia and worked as a sixth grade teacher in Fairfax County teaching math, science, and health in a Gifted/Talented Center. G/T Centers are 24/7 G/T all subjects grades 3-6. Highly gifted kids learn third and fourth grade math in third grade, fifth grade math in fourth grade, sixth grade math in fifth grade, and seventh and eighth grade math in sixth grade. That’s when I found my niche. I taught seventh and eighth grade math compacted into one year to highly gifted sixth graders, preparing some of them for Algebra 1 in seventh grade. Most of the kids progressed to Honors Math 7 and then to Algebra 1 in eighth grade. FCPS has several different math tracks, and they do a great job of offering enrichment and advancement in mathematics to those are are able. While that is a small percentage of the general population, it is an excellent way to let those students who excel in math to move ahead and take college math in high school. It was fast paced and challenging. I received professional development to prepare me and assist me, and I fell in love with math! Being an adult in a math classroom was a completely different experience than being a child in a math classroom. With my background in science, it all made sense and I was able to make more connections to the real world. Because of my background as a gifted learner, I was a good combination with the gifted kids. In addition to the fast paced curriculum, the kids did enrichment projects like City of Lights (scale models of DC buildings wired to light with bulbs and batteries) and Mathematician Expedition (a research paper on a mathematician of choice). We developed an understanding of the essentials in math, but we also discovered deeper conceptual understanding of mathematics in general.


My third position was in a middle school in Texas. I taught seventh grade, sixth grade Pre-AP, and sixth grade math. It was my first position at a middle school teaching only math. It was an excellent opportunity to focus solely on math education and to use new technology in math instruction. I co-sponsored the Math & Chess Club and worked with kids at a wide spectrum of skill levels. It helped me sharpen my focus on the middle school math years. The middle school years are an essential link in preparing students for high school math. The concepts go from concrete to abstract as students explore the use of variables and use multistep complex problem solving. Kids become fluent in fractions, decimals, percents, and integers. They explore proportionality and use formulas to solve geometric problems. They use basic number sense and calculation skills to solve more abstract problems.

I started tutoring math privately in 2001 and am focusing solely on tutoring now, both in person and via skype. I see math everywhere now. One-on-one tutoring allows me to individualize to meet each student’s needs. We start where the student is and we take it one step at a time from Pre Algebra through Algebra 2. Since I discovered as a teacher that I like math and understand math, my goal in life is to help others learn and like math, especially girls. It’s a heavily male dominated workforce, and girls are typically stereotyped not to like math. I am confident and enthusiastic and hope to share my love of math with my students. I hope to inspire them to feel confident in their skills and to pursue a college education, in whatever field they choose. They will need strong foundation in math no matter what job they do as adults.


My undergraduate degree was in science, and now I have specialized in math. I play chess and guitar. I do puzzles and listen to classical music. I expose my kids to math on a regular basis and point out everywhere I see math. They get tired of hearing me say ‘math is everywhere’, or ‘that’s math’, or ‘that’s science’, but it really is true. Math is everywhere and it’s involved in every job that every kid will do when they grow up. As an adult looking back on my own education, I wish the math requirements were then what they are today. I wish I or someone else noticed that I liked math and was good at it and that I had taken math classes in college. Now I love algebra and geometry. I picked up where I left off with logarithms. In 2007, I went back to school and took College Algebra at a local community college in Texas. I’m currently taking Trigonometry on www.khanacademy.org and want to take PreCalculus and Calculus when I am ready. With a husband and kids and a house to run, it’s not as easy now as it would have been to take those classes in college. But, it’s never to late to learn. I read somewhere to be happy, do what you love. I love math. So, I’m going to keep doing it!

30 Days of Truth: Day 27-What’s the Best Thing Going for You Right Now?

My family is the best thing going for me right now.  I’m in a really great spot. My husband has a great job as a health care attorney, and he recently made partner. My twenty year old stepson is in the Army stationed in NY. My nineteen year old daughter is a sophomore at Texas Tech and involved in her sorority (ZTA).  My twelve year old daughter is doing well in her seventh grade classes and dancing eleven hours a week. And my eight year old son is also doing well at school in second grade and amazes me every day with his intelligence and insight.

I’ve achieved the perfect balance of being a person, a wife, a mother, and a professional.  The house is quiet during the day, and I use the time to workout, to learn guitar, to write, to learn math, and to do all the work associated with running a household including the finances.  Once the kids get home, I’m busy with them, and I also tutor math part time. I love that I can use my education and still be a full time mom.  I don’t have any of the stress that comes with being a classroom teacher. Instead, I get to experience the enjoyment and fulfillment of working one on one with students on math-a subject I am passionate about.

I feel very blessed to be in my position, and I’m grateful because my husband and I envisioned this life and built it step by step together.

Pearls on a String

     “There is no such thing as a problem without a gift for you in its hands.”  ~Richard Bach
When things are difficult, we are really learning. Think about it. If everything was easy, would you learn anything? Psychologist Jean Piaget referred to the unsettling feeling of learning something new as “disequilibrium.”  When we already know something, we are in a state of equilibrium.  When we learn something new, we are in a state of disequilibrium.  Without disequilibrium, we don’t learn anything new.
Problem:  It was my second year teaching at a new school after returning from a six-year hiatus to stay home with my son.   I lasted through the first year and through the transition to a new grade level and principal the second year.  It was the Friday before spring break on my eighth year of teaching, and I had literally just taken a pie to the face in honor of Pi Day coming up on 3/14.  We gave up the scheduled day of curriculum to celebrate Pi and have fun watching brainpop videos about Pi and Einstein and competing in a Pi memorization contest.   I went to the office to file some papers during lunch to meet a deadline, and my principal asked if he could see me. He handed me a copy of a letter and said they weren’t going to renew my contract. He said that because I used the school’s online discipline system for issues like missing work and dress code and other behavioral infractions, that I was being ineffective and was not motivating my kids to do work.   He also said it was because my teammates didn’t think I was ‘happy’ and that I was not a ‘good fit’ for the student population.

Have you ever been told to do something and then gotten in trouble for doing it? Psychologists call it a double-bind. It’s a no-win situation where you are damned if you do, and you are damned if you don’t. Although shocked and blindsided, I realized in those moments that I was fighting a monster far bigger than I was. My crime was following directions, yet for some reason I was getting in trouble for it. I hung my head and cried for a few minutes, and decided that if he was putting me in that position, then I quit. I disagreed with the letter as well as the whole process of the team and assistant principals talking about me behind my back and planning to destroy my career without a benefit of a doubt or any willingness to help me in my perceived weak areas. It was clearly personal and political, and it was a bigger, more sinister monster than I wanted to fight.

Gift:  I walked away with my dignity and integrity knowing I followed directions and worked as hard as I could to be the best math teacher I could be.  I am now able to re-focus my energies on my family and my health and not feel the negative side effects that come from working in a toxic environment.  I know that I forged meaningful relationships with the students and motivated them to work.  If you know me, you know I love math. You know I love science. You know I love kids and teaching.  This negative experience helped me to sharpen my focus and to re-examine my professional philosophies.  It gave me the opportunity to spend time reflecting on the past and how to use past experiences to achieve future dreams.  I will not lower my standards or compromise my integrity for a flawed public school system.  Instead, I will work for myself and focus on teaching math, one-on-one without the interference of a highly politicized work environment.  I do believe that education is the key to success, and that learning never ends.  I still aim to teach kids to love math and to love learning throughout their lives, wherever their strengths may lie.  I am focusing on expanding my private math tutoring business and opening up a website in the future to help kids learn and love math.

Why tell this story?  I want to set the record straight that I quit only because they told me I couldn’t stay.  If any former students or parents are reading this entry, I want to tell them I did not quit on the kids.  I feel that they lost the most in this experience.  All of a sudden I was gone, and they didn’t know why.  I heard from one of my students a few weeks after I left, and she said the administration told my students I quit because I got another job.  I want all the kids and parents to know I did not get another job.  I only left because I couldn’t stay, and I didn’t know how finish the year when I didn’t know what to do day-to-day.   I want them to know it wasn’t because of them; it was because of the staff and administration.  I still believe in the kids, and I still believe in education. I will keep being me and keep doing what I do regardless of whether this particular school wants me or not.  I know who I am – and I know what I’m about, and I won’t let this negative experience destroy me.  I will use it as fuel to for purusing my dreams.  These are all pearls (of wisdom) on a string.

Ryan Adams “Pearls on a String”

Thanks for reading this entry. Peace out!

Change Happens

How many times have you wanted to freeze time? When you look into your baby’s eyes or when it’s the last day of vacation when life is so sweet you never want it to change, you wish that things could always stay the same so you don’t lose the feeling you have at the moment. But try as you may, time marches on. Babies grow, you always have to go back to work after vacation, summer turns into fall, trees lose their leaves and the landscape becomes barren. Hair turns grey, skin wrinkles, hard bodies turn soft. Waves come in and they go out. Rivers flow. Mountains erode. Animals evolve. People you love die, and life goes on. Change happens.

On the flipside, when life gets hard and things seem as bad as they can get, you wonder if they will ever improve. You wonder if you will ever feel better or if circumstances will ever change. The grass is always greener somewhere else. One of life’s challenges is to learn to go with the flow, to embrace the ever changing nature of the world and our lives. When things are bad, they have to get better, and when they are good, you wonder when something bad will happen. One thing you can be sure of is that tomorrow is a new day. Change will happen.

I’m reflecting on the changes I’ve been through and the changes I’m about to make. I morphed from a high school and college student into an environmental activist working for Greenpeace. I got married and got divorced, becoming a single mom. I got my master’s degree and got remarried and taught school for six years while raising two daughters. When we considered having a third child, I proclaimed I would only agree if I could be a stay home mom. It was already far too stressful working all day and then coming home to two children, a tutoring job, and a house to run. Joe finished law school and scored a great job at a large firm in DC, making it possible for me to stay home. I thought life would be paradise. I remember thinking I could go to Starbucks anytime, go to the gym, go shopping, essentially live like a princess. I envisioned the stereotypical sitting around eating bon bons scenario. When Thomas first arrived, it was wonderful not to have to work. I enjoyed the peace and quiet during the day and was able to nap and be on his schedule. As the years went by however, it started to get old. As Thomas got bigger and more independent, I started to get bored and lonely. I started looking for ways to fill my time since I had some extra time on my hands. I played a season of adult soccer and took a College Algebra class at the local community college. I published my dad’s book. I tutored math part time at home. Much to my surprise, most moms I knew worked, so my days became full of doing dishes and laundry and paying the bills and cleaning the house. Where did my princess paradise go? Thomas and I did some fun things together, but I found more and more I was missing adult relationships and was losing touch with my professional identity. Because I wasn’t getting up and going to work every day, I got used to the sporty look, you know, pulling your hair up in a ponytail and being ready for a workout at the gym. I started getting snide comments from pretentious women about my appearance. They didn’t seem to understand how or why I would be ok being seen in public without makeup and my hair done perfectly wearing shorts and a t-shirt. I’ve always felt pretty strong inside and even though I was taken aback by such rude comments, I tried to remind myself I live in Texas where being pretentious seemed to be in fashion. Besides feeling like a sore thumb surrounded by some rude barbies, I experienced frustration in other areas as well. Joe tried to warn me not to play soccer because I would get hurt, but I didn’t listen. He was right. I got hurt. I rolled my ankle running full speed then reinjured it later doing high kicks with Sierra, tearing a ligament all the way off the bone and tendons on both sides. I had two surgeries to fix my ankle and two more to fix torn cartilege in my knee as a result of the ankle injuries. I also had my appendix removed. That’s four surgeries in the four years we’ve lived in Texas. I passed my College Algebra class with a B after a lot of hard work and met some new friends only to lose one of them in a tragic car accident. My dad’s book was a success as was my tutoring business, but my kids hated it when I tutored. I worked Mon-Thurs after school from 4-6pm, and my kids resented the fact that as soon as they came home I disappeared behind a closed door and told them not to interrupt me. They didn’t care that was the way I made money. They just wanted my time.

Now, Thomas is about to start kindergarten (full day) and I am so thankful I found a job teaching 7th grade math. My life is about to change all over again. I start full time on Wednesday. I know the grass won’t be the greenest and nothing is ever perfect, but I do think it’s time I get back into society and use my education and skills and talents again in a professional setting. I worked really hard to get my master’s degree and am a licensed, experienced teacher who is capable of touching kids’ lives. My kids will be gone all day at school while I’m gone all day teaching, and when I get home I will be available to them. I can help kids learn to love math and still have summers and vacations with my own kids. I’m not sure how I will juggle all the work and responsibilities, but I feel I am making the right move.

There are many moments in my past where I wish I could have frozen time. There are many times I wish I could go back to and change, especially those moments where I lost someone dear to me. But I realize that’s not possible. Life moves on. Things happen, whether for a reason or not. I realize now that all I have is today, this moment. The past is gone and tomorrow hasn’t happened yet, so all I can really focus on is now. And what I want to do now is be the best I can be. I want to use every moment from my past to touch the lives of the future. I want to pour my love and energy into the people who matter the most to me, my husband and kids. I know that everything can change in an instant, and for now I should be grateful.

Keeping my kids busy in the summer

Yes I am one of those ‘mean’ moms who makes her kids do homework in the summer. I have always heard the schools say to READ, READ, READ over the summer, but what about math? What about spelling and writing? When I used to be a teacher, I was chair of the math committee one year and implemented a summer math program to run alongside the summer reading program. Each grade level made up packets that reviewed the key objectives from that year. I am now a private math tutor, and I highly recommend that all kids study through the summer months. They should review what they learned last year and preview what they will learn next year. When school starts they can hit the ground running, and teachers don’t lose precious weeks reviewing and reviewing because kids forgot what they learned last year. Every June, I go to the teacher store and buy “Summer Bridge” workbooks for my kids that span all subjects from one grade level to the next. My kids have to work for atleast an hour a day Monday through Friday in their books before they can watch TV or play Wii. The summer bridge workbooks stop after 8th grade. My teenager, who is a rising junior, works on PSAT instead. After all, knowledge is power, and after working for an hour or so a day they are free to do whatever they want and play around and/or be lazy for the rest of the long summer days. It’s good for them. Knowledge is power!

Dansk: Dedikeret til matematik

Dansk: Dedikeret til matematik (Photo credit: Wikipedia)