We live in a world that is so full of noise and information that finding silence is an arduous task. In fact, it has taken me over a decade to cultivate a consistent meditation practice. I meditate for two reasons: to hear God and to listen to my authentic being. Stopping the incessant chatter of my ego is easier some days, while others it is a hornet’s nest wanting to control the false narrative. My ego is critical, full of doubt, judgmental and insufferable. It is the voice that tells me I am not good enough, I will never be good enough and it will often wonder When will everyone find out that I am one big hoax?!  Thus, meditation is my tool for finding my balance, my joy, my essence, and my confidence. It is in the silence that I can find my center and see the gifts God instilled in me and the gifts I can offer to others.

Whether you believe (or not) in a higher power is not of my concern; what is of my concern when working with students is the narrative their ego is playing on constant repeat. Sit with any student and sooner or later the creature will breathe so loudly that the room vibrates. Its voice is so loud that it echoes in the silence. It can be stunning how quickly the ego turns on itself. This week I was working with a student and with one question the air was so sucked out that I was left breathless. One simple academic question shook the child of all her confidence and left her on the verge of tears. Before the beast of inadequacy could push us off the cliff, I told her that she needed to breathe. Breathing is a tourniquet to our inner critic. After a few moments, she was able to silence the beast and hear me. She had been studying fiercely for a high school placement test and was worried that it wasn’t enough. We talked about how her inner critic expects her to be perfect and work harder. Yet, it is okay to answer a question wrong or make a mistake; that is why we practice and study. We are not expected to be perfect. Life is messy and imperfect and to expect to do everything perfectly or get every question right is such a heart wrenching way to live. I told her that when her inner critic starts to criticize her, it is time to breathe (and deeply). I then told her that it wasn’t her perfectionism that will take her far, but rather her resolute work ethic. Her ability to digest large amounts of information is stunning and her work ethic is an inspiration. She needed to know that she is enough (imperfections and all). She needed to give herself the same grace she would give to others, while at the same time be able to recognize her talents.

I used to have another student named Keller who struggled with remembering math concepts long term. One week he would know his doubles or plus nine facts and the next week it was as if he had never been taught. He worked hard each week but his beast was always near him, whispering words of inadequacy and doubt. There were times when Keller believed that he would never grasp addition facts, let alone his multiplication. Yet, I can tell you that his effort to understand patterns in mathematics gave him a foundation that blew me away. Towards the end of our tutoring relationship, he was solving multi-digit and multi-step problems with incredible speed. He was able to store the strategies in his long term memory because he had created multiple pathways to access the information through his initial struggle. However, my heavy lifting during our sessions was not when I was teaching him about a math concept, but rather when his ego would roar about his inadequacies. This is where I become not just a tutor but a mentor to the child in front of me. This is where I teach the student in front of me to be a lion tamer. It is a time where I find not just the right words, but words that the student can believe are true to their authentic nature. It is finding the words to let them know that yes, school IS hard, but you are enough and you have the ability to attain knowledge with hard work.

In 1997, I was elected Student Government Assembly President at Metropolitan State College of Denver (now known as Metropolitan State University of Denver). A year or two prior to running for President, I met Zav Dadabhoy. He hired me to be the accountant for clubs at MSCD. Zav ran Student Activities and was the advisor to MSCD Student Government Assembly (SGA). He quickly became a mentor to me and I am forever grateful for our conversations in the Tivoli. He was quick to encourage me to run for Student Government and with nothing short of a miracle, I won.  Since Zav was also the advisor to SGA, he designed professional development and team building for the incoming assembly. It was an opportunity for us to put forth a strong agenda for students. It was during one of these sessions that we had to come up with one adjective to describe how we saw each person. It was remarkable and nerve-wracking to partake in this conversation where I was one of the ones being described. How others see us is usually so different than how we see ourselves. I cannot remember the adjectives my fellow SGA members used to describe me, but Zav’s adjective is forever burned on my third eye: untapped. Considering I had just won SGA President, being untapped was an interesting word to pick. He went on to say that he saw the potential in me and that potential was so great that this was just the beginning. That kind of description did something to my soul: it is a word that watered my soul with love and light. It is a word that creates sparks, an eternal fire, and hope. He saw in me what I hoped and thought was in me, but fretted I was wrong. Inadequacy is a beast that haunts us all. Yet, we have the power to see in others what we don’t see in ourselves. Being untapped has taken me far in life. It has given me courage to jump into the unknown more times than I can count. It has pushed me to try new things, and to spread my wings and fly.

I am forever grateful to Zav for so many reasons, but one is for giving me an internal spring of hope and potential. I strive to be Zav Dadabhoy to my students. I strive to find the essence of each child and then tell the child about his essence over and over so that he too has a word that waters his soul. I want every child to have a word that is innate and true to each person’s authenticity so that every child can go forward in the world without hesitation and doubt. Everyone should have a word that comes to them in the silence and that lets us know that we too are enough and more.


JoyThis summer, Karmin and I spent a significant amount of time researching both the little independent and large national tutoring companies. What struck us both as unfortunate was that the large national companies were focused on the bottom line; they discouraged individual tutoring so as to have each “teacher” work with a group of students as the students worked through a binder.

While group tutoring can be beneficial, it is only when the group is 3 or less children, all of whom are on the same conceptual level and are learning similar topics. Furthermore, having students work solely from a binder of worksheets is not the best way to individualize learning, nor does it excite kids and create a love of learning.

The intention of this post is not necessarily to bash the large tutoring companies, but rather to highlight the joy that we find on a daily basis when students are given the opportunity to delve into authentic learning. There is also a great amount of joy to be found when one learns that struggling and persevering leads to accomplishments, a feeling that cannot be re-created in completing a worksheet.

In any given week, I work with students from pre-school age to freshmen in high school. To this end, it means that my work with students ranges from number identification to quadratic equations. Just tonight, I worked with a four year old, a fourth grader, and then a third grader. The four year old expressed immense joy as she could use one-to- one correspondence with numbers up to 9. My fourth grader had endless smiles because after the last year of school spent where he was told that he wasn’t a proficient math student, he now was formally recognized as one of the top math students in the entire grade. And finally, my third grader kept shrieking that now that she sees so many amazing patterns and connections in numbers, that she wants to do math everyday, including the weekends, for the rest of her life!

This, my friends, is joy. Sometimes it’s easy to wish that the education world brought a six-figure income, but when I realize that I have the capability to help create that much love and fun in learning, there isn’t a thing in the world that I would rather do.

Recently, I have watched so many friends (including myself) leave teaching because the joy of learning is being sucked out of what we are able to do each day in the classroom. I am so grateful that Karmin and I took the leap to create Mathletes & Bookworms because it has not only allowed me to expand my world of teaching, but has really given me the ability to spread my wings and watch as kids change their views on life-long learning. Joy.


Image from https://www.theodysseyonline.com/choose-joy-feeling

Be Fierce

Since February, I have begun a new workout at a place called Fierce 45.  It is a local studio that uses the Lagree Method.  The easiest way to explain it is a 45 -minute workout that’s Pilates on super-duper steroids.  Although I’ve spent most of my adult life working out in various ways (marathons, weight lifting, P90X, Insanity…to name a few), this is by FAR, the hardest and most effective workout I have ever done.

What does Fierce 45 have to do with learning math (or any other subject, for that matter)?  At the beginning of each workout, there’s a chalkboard where each person writes his/her name and intention.  The purpose of the intention is in knowing that the class is going to quickly get to a place where one doesn’t think they can finish and rather than giving up, can remember what brought them there in the first place.  It’s amazing how this happens in every workout, and I must tell my mind that I am strong and can do hard things.  Plus, I know that I have survived it before and can do it again.  Even better, I can bring this mental strength outside of the studio to tackle other hard moments of my life because I know what I am capable of.

A lot of times, both children and adults shy away from math because it is “hard.”  While this is 100% true, it’s important that our students have the mental fortitude to tackle all subjects if/when they become difficult.  We are way more capable than we usually give ourselves credit for.  Unfortunately, what sometimes happens is that kids feel so pressured to do things quickly and correctly the first time.  But that’s not the point.  The point is to emphasize that over time, even despite struggles, we will conquer the things we set our minds to.  Sometimes this can take more time than we realize.

My last teaching job was at new school called Aurora Quest K-8 where I taught 6th/7th grade math for gifted and advanced learners.  This past May, the school had a reunion as the first Kindergarten kids in the building were graduating from 8th grade.  The kids from my last class were graduating from high school and many came to the reunion. It was a night I will never forget, as so many students told me that while they struggled with math in 6th grade, they had learned to value the struggle and many had ended up liking AP calculus.  I had students going to schools like Stanford, Cornell University, and Yale to study math related subjects.  Trust me when I say that there were many days when these then 6th graders had written math off as too hard and not useful.  But what had obviously occurred in the last 6 years was an acceptance of the struggle and appreciation of its value.

Just as every time when I go workout, I get to a place where I want to give up, we must recognize that students are going to go to that place also.  Instead, we must help them cultivate the strength to push through the hard moments, even if they don’t always pay off.  Because the next time, that knowledge just might be the very thing that gets them where they need to be.

Visit www.fierce45.com if you are interested in giving this workout a shot!  Tell them we sent you 
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Learning to Fly

“Karmin, all of the work we did this summer prepared me for class!” Lucy exclaimed excited as we started our weekly tutoring session.

“Awesome, that is why I am here to support you,” I replied.

“Yeah, in the past it was only the smart students who answered the questions in class but now it is, you know, people like me,” my student replied sheepishly.

A knowing smile crept into my eyes as I replied, “Lucy, you are the smart student. You have always been smart. However, you have been working incredibly hard over the last couple of years and it is paying off.”

Several emotions danced across Lucy’s face: the shock and realization that she is a mathematician, coupled with immense pride. This is why I teach. It is the joy of having a student who was once struggling find solid footing in academia. In truth, this conversation is only the tip of the iceberg of Lucy’s growth. Over the last year, I have been working with Lucy on study habits, organizational skills, and a heavy focus on mathematical concepts. What has emerged is a young lady that is becoming organized and prepared for academia.

One evening last year, Lucy described her struggle to prepare for Spanish tests and asked if I could help her study. While I am not fluent in Spanish, nor am I a Spanish teacher, I told Lucy and her parents that I would be happy to discuss study skills that would be applicable to Lucy’s Spanish test. We discussed similarities and differences in how a student would prepare for a Spanish test versus a math test. A similarity is that in math we practice problems that would be similar on a test such as using orders of operations and in Spanish she could write similar sentences using vocabulary and specific verbs. The difference Lucy explained was that there was a lot of vocabulary and there were certain words that were eluding her. I said we could use flashcards to help her connect the ideas. I explained that writing ideas by hand is more powerful than typing on Quizlet or on another online app because of the mental work involved.  In fact, Cindi May wrote in Scientific American,

“What drives this paradoxical finding?  Mueller and Oppenheimer postulate that taking notes by hand requires different types of cognitive processing than taking notes on a laptop, and these different processes have consequences for learning.  Writing by hand is slower and more cumbersome than typing, and students cannot possibly write down every word in a lecture.  Instead, they listen, digest, and summarize so that they can succinctly capture the essence of the information.  Thus, taking notes by hand forces the brain to engage in some heavy “mental lifting,” and these efforts foster comprehension and retention.  By contrast, when typing students can easily produce a written record of the lecture without processing its meaning, as faster typing speeds allow students to transcribe a lecture word for word without devoting much thought to the content.”


Lucy went on to write out notecards and then we did some exercises that helped her memorize the vocabulary. We filtered out words she that easily retained and kept the more stubborn words that would not stick. The following week when I saw Lucy she was overwhelmed with excitement because she had scored in the 95th percentile which was the highest grade she had received to date in that class.

This summer Lucy had assigned reading. As July was coming to an end and August neared, Lucy was concerned about completing the two books she had left before school started. She was both overwhelmed and scattered between the two texts. Together Lucy and I worked on a calendar and broke the books and accompanying writing assignment into smaller chunks that would allow her to get through the assignments before school started with ease.  During those last weeks of summer tutoring, Lucy had the plan we designed on her desk and had check-marks on completed assignments. One week she told me she was behind by a day because she had a sleepover but wasn’t worried about it because she had planned for extra time that afternoon to complete. After the initial plan was designed, Lucy was able to take control of her own schedule and make adjustments necessary to still have summer fun but complete her work in a timely manner.

What has emerged over the years of working with Lucy is a student who is not just a better mathematician but a better student overall. When Mathletes and Bookworms Tutors work with students, we are always working on a single subject but we strive to create responsible, engaged, motivated problem solvers. Not only do we want our students to strive in the subject matter we are working on, but also take the skills we teach and apply them to other facets of their life. Building academic confidence also builds social confidence. Having students understand that math is hard but that they can do hard things also allows them to stand up and do the right thing socially. What we strive to do in our sessions is meet the whole child where they are and help them find their wings. Lucy is finding her wings and I am excited to watch her take flight.


Image from https://www.healthytreefrog.com/the-swan-queen-changes-transformation/transformation/

Although the digital age has given us instant gratification, learning still isn’t

“I know it is hard; you can do hard things!” 

“I see you are struggling; struggle on. You are so close!”

These are phrases that Meghan and I find ourselves saying to students of all ages and in all subjects. They are the crux of what we believe and try to develop in our students. We want them to know that developing grit, confidence, and understanding is work. Whenever I am working with a new student and I acknowledge that their task is difficult, I get a look that is a mixture of astonishment, relief, and doubt. Without saying a word, you can see their thoughts clear as day, You are agreeing with me?! It is okay that I am struggling?

Children today are born into a world where information, products, and ideas come at them instantly and constantly. Answers are easily accessed on Google, smart-watches instantly update us on our health, on-line shopping delivers to our door next day, and the list goes on and on. You name it, we have made it: instant, instant, instant. Yet, understandings do not always come instantly and it is disheartening for children. They assume that they should just “get it” or “know it”.

In a world where everything is at their fingertips, it is believed knowledge can just be transferred through osmosis or at least with ease. It is only a matter of time before students realize that this idea is false and that learning is hard work. At this moment, it is vital for teachers to reach out and help students face this new reality by acknowledging the difficulty of the task and encouraging the child to keep persisting.

What we strive to do in our tutoring sessions is create problem solvers, thinkers, mathematicians, readers, and writers. Most importantly, we want to create confident students who recognize they are capable of doing hard things and doing hard things means there will be a struggle. We want students to understand that struggling does not mean they are less than/unintelligent/unqualified, but rather that struggling is an opportunity to grow, acquire new ideas, and test out problem solving skills.

There is a fine line between letting students struggle and pushing them over the figurative waterfall. Soviet psychologist Lev Vygotsky introduced the idea of Zone of Proximal Development (ZPD) in 1924. “The zone of proximal development is the gap between what a learner has already mastered (the actual level of development) and what he or she can achieve when provided with educational support (potential development)” (*Coffey, http://www.learnnc.org/lp/pages/5075). This is often referred to as the “Goldilocks Principal,” because the learning should be “just right.” As a teacher, it is of utmost importance that the student’s struggle is within his or her own ZPD. It is within this “zone” where students can cultivate grit, confidence, and problem solving skills. It is that edge of discomfort where they discover that they are capable of anything and that their dreams are achievable.keep-calm-and-struggle-on-5

Image from: https://www.keepcalm-o-matic.co.uk/p/keep-calm-and-struggle-on-44/

I have a confession to make


When I got my first teaching job it was teaching 5th grade, all subjects. Although, I had initially been terrified of the 5th graders in my student teaching, once I realized how interesting, smart, and mature (comparatively to the little ones who cannot tie their own shoes) they were, I felt like I had hit the jackpot.  As a result, I was pretty confident that I would never teach kids that were younger.

I taught my first three years with a principal whom I adored, after she left and before my 4th year, someone very different replaced her.  It was a difficult transition as Karmin and I were in the middle of a large research project with our previous principal and Washington State University, looking at how English Language Learners (ELL) learned math. We had just presented and published a math education research paper in Prague and were continuing on with the professors on another endeavor. This new principal took note of how much I loved teaching math, as well as having the gifted and talented (GT) cluster in my classroom.  Additionally, I had just become the building GT leader and I think she saw that I might have had my eyes on what was next.

To this end, somewhere in the late fall, she told me that I needed to start considering teaching a much younger grade the next year.  She said that if I wanted to be a building math coach or do more work with GT in other schools, I needed to have the experience teaching other grades, especially something different from the 5th graders.

I vividly remember going out to dinner that night with my then fiancé (now husband) and his mom, who was visiting from out of town.  I dominated the conversation about how absurd this idea was.  I likened it to a pediatrician all of a sudden having to take geriatric patients.  It seemed like another profession entirely, and I wanted nothing of it. I had grown so used to the more “sophisticated” concepts that my 5th graders were learning, and didn’t want to go teach the “basic” or “simple” concepts that the younger students were learning.

To make a long story short here, I ended up leaving that school at the end of that year to go to my district’s brand new GT K-8 school.  At this school, I would go on to teach 4th grade math for one year and then 6th grade math for two years. I left teaching after 7 years to start Mathletes & Bookworms and have since worked with children from age 4 to 14.

Now that I have 13 years of teaching and tutoring behind me, I can say, without a doubt, that I would not be the strong math teacher that I am without having the breadth and experience of teaching and tutoring kids from Pre-K through 9th grade Honors Geometry.  I see so many places where math teachers fall short because they cannot see how everything is linked.  When I am doing combinations to 10 with a very young child (for example, 3+7, 5+5, etc.) on Ten Frames, I am able to see where that child needs to be in pre-algebra, algebra, geometry.  Likewise, when I am working with a struggling student in pre-algebra I can see what gaps need to be filled quickly and it usually goes back to early number sense. Working with all of the different ages in math has completely revolutionized how I see and think about math.

Unfortunately, math education has a couple of areas in which it needs major improvement.  First, it is imperative that all teachers, from K-12, have strong math understandings.  I’ve met a lot of teachers in the K-2 grades who have decided to teach those ages because they are “afraid” of 4th and 5th grade math.  This really concerns me because those teachers need to prepare the students for what is coming.  I am not saying that elementary math teachers need to know calculus (heck, I would need a very long refresher myself!) but it is essential for teachers to see the next steps their students will need to take. Additionally, it should be mandatory that teachers change grade levels every few years. Not only does it give one a much greater perspective (of all subjects, not just math), but could prevent some of the burnout that exists when doing the same thing, every year. Change is where true growth and new understandings are found.

So if I could find that principal who told me in 2007 that changing grade levels would be the best thing for me as a teacher, I would tell her that she’s right.  That while I used to be a good math teacher, now I think I am a great one, and that is solely due to my work with so many ages.


Image from: http://homeliving.blogspot.com/2015/01/back-to-my-little-corner-of-world.html

“. . mathematics is not just another language . . . it is a language plus logic. Mathematics is a tool for reasoning.” Richard Feynman

To be a good mathematician is to be both creative and logical. Everything in mathematics comes back to a basic foundation of problem solving.  It is not the many answers you know or memorize, but rather how you attack a problem when you don’t know.

There are times when we sit with students and come across a problem that we do not know how to solve immediately. The student is always shocked.  “You don’t know how to solve this problem?!” they ask incredulously.

Proudly, we tell them, “No, no I do not.”  We say this with a believable confidence because we know it is an important lesson for all students to learn at an early age. No one has all the answers, whether mathematicians, teachers, adults or anyone else that students perceive are the “all-knowing people.”

What makes us successful teachers is that we know how to problem solve. So often, the crux of the problem solving comes from the most basic of mathematics.  For example, a student may be doing an algebraic equation, solving for “x” that has fractions in it.  A lot of it goes back to strong number sense, the power to break apart numbers which leads to a strong understanding of factors and multiples.  Without this, all understanding of fractions, never mind solving for “x”, falls apart.

People falsely believe that they are either good at mathematics or they are bad. They see it as black and white.  This idea is frustrating for several reasons. To start, a pianist does not say, “I am a bad pianist; it was just the way I was born.” Nor, does the mother say, “I am a bad mother, I never understood it.” No, what a pianist does is practice, practice and then practice some more. When parents are struggling with a particular piece of parenting, they do research, talk to people, and find ways to improve their parenting skills. Unfortunately, America has made it socially acceptable to say, “I’m not a math person” or “I am bad in math.” It should be an insult to our ingenuity as a country to weave this kind of thinking into who we are. Our history is steeped in those who are problem solvers; those who pride themselves in doing hard work and developing grit.

We need our children to know that everyone is a mathematician. Everyone is a problem solver and most importantly to know that logic and creativity aren’t genetic gifts, but rather skills to be developed over time. The greatest joys we see in our work is when kids realize that this isn’t a “locked” door, with the key only available to some.  It is an open door, and one that leads to an infinite number of places for everyone.


Image from: https://www.dreamstime.com/stock-illustration-bright-sketchy-doodles-brain-colored-elements-image50332839#