Tag Archives: learning

Paul Lockhart’s Lament

During the first days of summer, I usually catch up with my guilty pleasure TV shows and get a few projects around the house completed.  However, I found myself jumping into my first book “A Mathematician’s Lament” by Paul Lockhart.  It is sold on Amazon, but I also found a PDF here. Someone on Twitter had posted a quote from the author and it spoke to me.

Lockhart jpg-large

Why did this speak to me?  During the NTCM 2018 Regional conference in Seattle, Christopher Danielson gave a talk on the word “play” and how playing unofficially becomes the 9th standard of math practice.  Play is such friendly, non threatening word.  Play gives people permission to explore freely.  Unfortunately as we grow up, sometimes we forget that element from our childhoods.

Screenshot 2019-06-19 15.11.58

Back to the Lament…as I started reading Mr. Lockart’s Lament, I wondered when it was written.  According the Keith Devlin’s forward, it was written in 2002.  This little fact fascinated me because this was written 17 years ago.  17 years ago, I was a 3rd year teacher learning about the STAR (Standardized Testing and Reporting) and the CST (California Standards Test).  This was a time of teaching facts and tricks.  We memorized formulas.  We taught strategies of how to get through the multiplication test.  Do you recall “No Child Left Behind”?  It was a time of too many standards to teach and not enough time for depth.  I shudder thinking about how mechanical teaching was and time to “notice and wonder” where far off into the future.

What struck me about Mr. Lockhart’s statements were that it’s still relevant to today.  There are many of us in the math community that are trying to be “math rebels”.  We don’t necessarily need textbooks and tests.  Those entities kill the beauty of mathematics. And it’s those entities that make students hate math.  No one has shown them that it’s one big puzzle that you have to keep hacking away and understanding the “why” of it.  The beauty of mathematics shouldn’t be brought down by drill & kill worksheets, timed multiplication tests, and useless work.   As Mr. Lockhart says, “mathematics is the purest of the arts as well as the most misunderstood.”  Would we deaden a photography, ceramics, sculpting, painting, or ballet class with a worksheet?  Can you imagine?  So why are we doing that with math?

And so I found it refreshing to read this piece because I like finding kindred spirits of the math kind who have similar views like myself.  Paul Lockhart and Jo Boaler have both given me relief because I thought I was the only one out there with similar thoughts.

Here’s a section of the book that caught my attention the most.

By concentrating on “what,” and learning out “why,” mathematics is reduced to an empty shell.  The art is not in the “truth” but in the explanation, the argument.  It is the argument itself that gives truth its context, and determines what is really being said and meant.  Mathematics is the art of explanation.  If you deny students the opportunity to engage in this activity–to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations—you deny them mathematics itself.” 

I implore you to read it yourself.  Ponder what’s going on in your classroom, school, or district that would deny students the beauty of the math.

Happy Summer everyone!

Until next time,


NCTM 2019 San Diego

It’s Monday night and my head is still reeling from all that I learned, experienced, and witnessed at NCTM San Diego.  Whenever I go to such a big conference, I just act like a sponge and soak it all in.  NCTM is a place where we all learn from each other.  I haven’t been to the NCTM Annual conference since 2015 in San Francisco.  That experience just left me inspired to be the best math educator I could be.  Sounds corny…right?  But it’s completely true.

I left with a bunch of take aways and would love to share a few of my favorites.

Graham Fletcher

  • Do we want to be teachers who learn math to solve problems to solve problems to learn math?
  • Speeding doesn’t get us to where we want to go faster
  • Estimate = strategic choice of a number
  • be intentional and purposeful with choosing tasks, don’t have a one night stand.

Kassia Wedekind presented a session on hands down conversations.

  • Invest in turn and talk partnerships
  • (can’t wait to try that in my classroom).

Sara Van Der Werf – The Matthew Effect

  • “the rich get richer and the poor get poorer”
  • those who start school with a small advantage continue to benefit, while those with a slight disadvantage continue to lose ground.
  • Teacher will LEAD the way to change structures so all students are successful.
  • How will I support student who arrive to school without the advantages some students have?
  • IMG_5576
    Sara Van Der Werf – tall math girls stick together!

    One of my favorite quotes I saw was in Sara’s presentation.   And I left with much food for thought….how can I do better? How can I advocate for all my students no matter who they are, where they’ve been, or where they are going?

Maya Quotes 3

 At ShadowCon, I saw Bethany Lockhart, a kindergarten teacher who spoke about risks worth taking and trying a #BraveBoldMathMove.  She was a phenomenal speaker.  

I also saw Chrissy Newell speak about #MathGals.  As a matter of fact, I bought the book “Power in Numbers” because of this.  

Day 2 featured a great talk about PhotoTalks by Beth Barnes.  Also saw Jennifer Moffett do a session on Middle School Clotheslines.  Jennifer asked the question of “What do instincts have to do with math?”  Math inspires curiosity and we try to make sense of things.  

By Day 2 of the conference, my brain was starting to fill super saturated, so I didn’t take as many notes as I would have liked.

It was a bummer that I didn’t make it into the exhibit hall.  I would have stopped by the MTBoS table to get some goodies, but I was having a ball learning from so many great minds.

Until next time,


Making sense of conversions

My son, Jared, is in 6th grade.  He has told me he thinks it’s “cool” that I’m teaching 6th grade too.  According to him, we have stuff to talk about.  I can finally help him with his homework.  (Really?  Like I’ve never been able to help you with any of your other homework?!?  What the what?!?!?).  Of course I left that last editorial in my head, but I think I knew what he was talking about.   I think he meant that we are finally at the same grade level as teacher (me) and student.  

On one evening, he was having trouble with conversions of measurements. This was his homework.IMG_6073

I asked him about his notes from class.  “How did your teacher teach this?  Where are your notes?

And this is what he showed me.

“Memorize the 3 steps.” Uh–no.

 I was not thrilled to see “memorize” on my son’s notes.  It dawned on my husband and I that our son’s teacher has only been teaching a few years.  He’s probably used to just memorizing steps and procedures.  I don’t like to teach that way.  I like to teach for understanding.  I like to teach more conceptually.  I like to have my students make sense of a problem rather than “memorize” steps.

Just for kicks and giggles, I went to page 290 to see what is said.  This is what I found.

Here are the “steps” my son was asked to memorize

I sat and stared at his paper and at the “steps.” If my son didn’t understand and remember the steps, how could I get him to comprehend what they were asking?

I looked at the 1st question again.  “If 16 C = 1 gallon, then 8 gallons = ________?”  Rather than doing a fancy algorithm or proportion (which he hadn’t done in the curriculum–my husband had an issue with that.), I went back to the basics.  Let’s draw a picture.  


16 cups are in one gallon (rectangles).  8 gallons with 16 cups in each.   Once I sat and explained the situation to my son, the lightbulb went off in his head.  “Oh mom, all you have to do is multiply 16 times 8 to get the number of cups.”  BINGO!  

And the rest of the hour, we drew pictures, diagrams, and whatever else helped him make sense of the conversions.  And each time we drew a new picture, the lightbulb kept going off in his head.  (Proud Math teacher and Mom!)IMG_9373

The next day after school, I asked my son if his teacher said anything about the homework we did.   My son told me that his teacher said,you should have done it the way I told you too.”   ARE YOU KIDDING ME?!?!?

I “heart” Tina Fey.

MATH RANT – –   After close to twenty years of teaching math, this just blew me out of the water.  It is no secret that there are many ways to get answers to math problems.  I usually give the anecdote that there are many ways to get from here to New York.  Some ways are faster, some ways are slower, some ways are more expensive and that’s ok.  Pick which way works best for you…..as long as you get to NY.  Same goes for math.  It is our job and soul purpose to teach our students.  It is well known that one size doesn’t fit all.  One approach to solving conversions doesn’t work for everyone.  Why are we still having students memorize procedures if they don’t understand the problem?  What happened to making sense of things? It only happens to be the first standard of math practice!!!    It baffles me that this is from a newer teacher who hasn’t done any conceptual lessons and/or applications.   The whole thing blows my mind! Maybe it’s also the realization that not every math teacher thinks or teaches like me.  

So what do we do?  Do we challenge teachers like this?  Is it worth the fight when they may not understand the importance themselves?  

My son’s situation just proves that there’s more work to be done out there.  Teachers still need training.  And just because we, in our youth, learned to memorize procedures, doesn’t mean we actually made sense of things.  

Math rant over. Disengaging.  

Until next time, 


Deep thoughts…

Last weekend, I attended a memorial service and a birthday party on the same day.  The range of emotions went from sadness and tears to laughter and smiles –all within hours of each other.

Of course during the service, my mind started wondering to all sorts of places.  The deceased was a father of a teacher who had encouraged his children to get a college education.  Upon hearing this, thoughts of how I became an educator started entering my mind.  It was my father who told me “Education is the one thing that no one can take away from you.”  That one piece of advice has been my mantra during my career as an educator.  And it’s importance seemed so tangible that I wanted to be a part of it.  I wanted to pass on such knowledge and make a difference in childrens’ lives.

Education is a gift to all of us.  We have heard that adage of “it takes a village to raise a child.”  There’s beauty to that sentiment.  We are all educators–whether we are teachers, parents, grandparents, young, old, male, female, or human beings.  We all have something to teach and instill into each others lives.  We all have something to learn from each other.  Some of us—myself included—have been fortunate to make a career out of it. It’s an extraordinary feeling to instill one memory, one quote, or one smile into someone’s life.   I knew of the joyous feeling of teaching teenagers for much of my career, but now my work with adults is even more satisfying and humbling.

And that brings me to the birthday party I attended later on that evening.  The festivities was for a former student who looks to me as her mentor.  She was one of my favorite students of all time.  Why?  Because she may not have been smartest or fastest math student that walked into my class.  But she was one that showed the most heart and gave me the most effort.  She was/is the definition of integrity.  She made me strive to be better teacher.   And I have found that those kind of students are few and far between.  And as an educator, you never know what kind of impact you have made on any child.

And so, as I sat there at her Sweet 16 party, I didn’t see my former student.  I saw a young woman whom I was lucky enough to cross paths with.  I sat there with pride because I had something to do with her life.  I hope that I made a difference in her life as I did with many others.  I hope everyday that I’m making a difference when I coach my teachers with their math curriculum.  I hope that the joy, the excitement, and my love of math (#mathnerd) gets passed onto them.

I’m suddenly lost for words as to how to close this essay/blog post.  So instead, I decided to include pictures of past students, current students, and people who have been educators in my life.  I write this with the greastest humbleness because not only have I’ve been their educator but they have been mine.  All of these people inspire me to be the best teacher I can be.  We all have something to learn from each other….and I’m grateful to be any part of that learning process.

Until next time…keep learning, keep educating, and make a difference,


One of my students is a professor! Holy PhD!



My mother and father were my first educators.  And I’m always learning from my husband and my son.