Transcript

You hear the whoosh of 25 Sprints flip over, followed by the urgent scrape of pencil on paper - fifth graders doing math.  Save for some twitching lips, all mouths are closed.  Concentration is deep, adrenaline high.  The students are grounded in the moment.

Watching this video, you likely have one of two visceral reactions.

You might see a white dictatorial man imposing his will on children, using his professional and physical stature to conform his students into computational soldiers.  The classroom is his bootcamp and the students are obedient, pencil-wielding cadets.  You’re quite certain that one day many of these children will feel traumatized by their fifth grade math experience.

Conversely, you see every single fifth grader in a title one school excited to document and show off what they’ve been learning for the four days prior.  Instead of a drill sergeant, you see a rigorous instructor who has prepared his students to learn more complex topics later in the class period and following week.  The classroom is a stage and the students are actors, performing what they’ve practiced, celebrating what they’ve learned.  You’re positive that these children will do well in middle and high school because of their fifth grade math experience.

Depending on your educational beliefs there could be shades of truth in either reaction.  As the teacher in the video, I clearly favor the second perspective, but even that is complicated, because they weren’t my students.  I was guest teaching in a first-year teacher’s classroom.

Over 11 years have passed since that video was filmed.  Experience has matured my ideas of what works and I now understand that individual learning activities are received differently depending on the circumstances, school, and student.  Sprints are no exception.

Still, it’s unwise to make sweeping generalizations based on truncated optics.  To fairly critique any event it is necessary to attain a deep understanding of what comes before and after that which we’re judging.  Cable news programs prey on the lazy human tendency to believe “What you see is all there is” and this video which has over 30,000 Youtube views can have the same deleterious effect.   Some love what they see, others definitely do not, but very very few fully understand it.

This episode of Centering the Pendulum aims to change that.

Pendulum Transition

I was introduced to Sprints in August of 2006, when I was trained in elementary math teaching methods by Dr. Yoram Sagher, professor of mathematics at Florida Atlantic University.

During the training, I learned that Dr. Sagher developed Sprints after spending extensive time observing Chicago public schools.  Too often, he found himself sitting in on classes that began with student passivity rather than activity, with boredom rather than engagement.

Robin Ramos:  I have seen so many classes start conceptually with Well what’s your prior experience?  Or What do you know about?

That’s Robin Ramos, the lead writer of Eureka Math’s Pre-K through fifth grade A Story of Units curriculum.  While she was a math coach at Ramona Elementary school in Los Angeles, she was trained in elementary math teaching methods by Dr. Sagher.

Robin Ramos:  Fourteen hands shoot up because they want to talk about their uncle’s tiling business or you know they remember a time in second grade when. . . and then everyone has to share and everyone’s bored.

Students, Dr. Sagher realized, need to be engaged and doing math immediately upon entering class.  Initially, he recommended beginning with an ungraded quiz.  This provided a more centered start to the class period, but two other problems persisted:  Classroom energy remained relatively low because many students were unmotivated and children were still not getting enough practice.

This helped him pinpoint two major problems with elementary school math students in America.

Dr. Yoram Sagher:  First, they do not concentrate well.  Secondly, they aren’t doing 100 practice problems a night.  Sprints address both of these issues.

In his book, Teach Like a Champion 3.0, best-selling author Doug Lemov writes that an effective Do Now should meet three critical criteria to ensure that it’s focused, efficient, and effective.

1. The Do Now should be in the same place every day so it becomes a habit for all your students.

2. Students should be able to complete the Do Now without any direction from you, without any discussion with their classmates, and in most cases without any materials beyond what they always bring to class.

3. The activity should take about five minutes to complete and should require putting a pencil to paper.

A Sprint routine run well checks the first two boxes, but not the last, because they normally take eight to 11 minutes to deliver.  A different way to see Sprints might be as an extended or lengthier Do Now.

Pendulum Transition

Growing up in the eighties, fact retrieval practice was an integral part of my elementary school math classes.  Weekly timed tests and the flashcard game Around the World sent my classmates and I a clear message:  Automatization is an expectation and with some teachers the end goal.  Vestiges of this outlook remain, but it’s nearing extinction.  Today, most elementary educators agree that students need to understand mathematics, not simply get answers right through systems, mnemonics, and procedures.  Within this shared philosophy, however, there are wide ranging opinions as to how this is best achieved.

Eureka Math recommends a balanced four-part lesson that includes fluency, problem solving, direct instruction, and reflection while other curricula advocate for an inquiry-based approach.  The pursuit of the same goal, therefore, looks very different depending on preferred pedagogy.  The onset of the common core era, it seems to me, can be defined as a sorting out period in which we’re all trying to figure out the purpose of the subject. 

So divided is the elementary math community that we haven’t even reached a consensus as to whether or not it’s useful for children to commit basic computation to memory, much less use class time to practice it.

I believe that strong number sense and efficient calculation is an enormous advantage for any child learning math and those who struggle with either or both are severely limited when studying the subject.  But my opinion is fairly meaningless.  So, rather than leaning on my teaching experiences, I’ll defer to real experts.

Dr. Scott Baldridge:  It’s really important for example that the children eventually get to a point where multiplication of the like say the one-digit facts is instantaneous. 

That’s Dr. Scott Baldridge, a research mathematician at Louisiana State University and the architect of Eureka Math, the most popular K-12 curriculum in the U.S. 

Dr. Scott Baldridge:  And the reason for that is this thing that goes on in our brains which is called “chunking.”  If you’re going to attack a much bigger problem that’s going to occur in seventh grade or eighth grade.  A four-step problem, a five-step problem and so one of the techniques for a child to take on a much harder problem is for them to be able to look at a given situation and even if they don’t know what the multiplication is going to eventually be, they know that they can find it.  It’s not going to be a deal breaker that they don’t know what three times seven is.

Dr. Baldridge’s protégé, Ben McCarty, a research mathematician at Memphis University shared this.

Ben McCarty:  You do need those components to be in place so that when you start doing the algorithms for example you don’t want the kids sitting there trying to figure out how to multiply six times seven while their trying to work out what 46 x 57 is.

Doug Lemov had this to say:

Doug Lemov:  If you can do computational facts very quickly at almost no load on working memory you can think more deeply about Is there an easier way to solve this?  Is there a better way to solve this?  What exactly is it that I’m doing right now? And if you can’t do those things your working memory will always be used up just in the calculation.

In his acclaimed book, Why Don’t Students like School, world renowned cognitive scientist Daniel Willingham wrote, “the bigger storehouse of information a brain has, the better the brain will comprehend information coming in. . .thus allowing more thinking to occur."  In a separate essay, he stated "automatic retrieval of basic math facts is critical to solving complex problems because complex problems have simpler problems embedded in them.”  He went on to say, “if we reduce work on facts. . .the result is likely to be disastrous."

But all of these comments stray a little off topic.  Automaticity can be a byproduct of using Sprints regularly, but it’s hardly their intended purpose. Sprints are a tool and system designed to increase fluency not robotic automaticity.

What is mathematical fluency?  Well. . .it’s a lot  easier to recognize than define.

Fluent students are good at arithmetic, but haven’t necessarily automatized computational facts.  Instead, they possess a more holistic skill set that allows them to efficiently arrive at answers through multiple pathways, which they effortlessly select and toggle between.

Duane Habecker:  When I’m thinking about fluency I’m thinking about the presence of 4 things.

That’s Duane Habecker, founder of Embarconline.

Duane Habecker:  Speed and accuracy.  I’m also thinking about flexibility and I’m thinking about appropriate strategy use.

Here’s Robin’s take.

Robin Ramos:  So much about mathematics is making connections or seeing relationships.  I have to see the relationship of five frogs and three frogs and five-eighths and three-eighths and then that I can make a higher value unit.  So, it’s like these basic concepts of breaking numbers apart putting them together and seeing those so that you get a fluency with recognizing relationships.  And so the fluency of being able to think in different ways and it feels like training for the brain you know.  It’s not just about mathematics.  It’s about getting the brain to be facile.

The idea of arithmetic being good training for the mind is an ancient one.  In his book, The Republic, Plato explained why the understanding of mathematics was critical to entering the academy.

Plato:  No branch of education is considered so valuable a preparation for household management and politics, and all arts and crafts, sciences and professions, as arithmetic. Best of all by some divine art it arouses the dull and sleepy brain, and makes it studious, mindful and sharp.

There are a myriad of methods to practice different topics, so why did Eureka choose Sprints to drive fluency at every grade level?

Robin Ramos:  What went into Eureka is what I saw work.  The Sprints got everyone involved at a level they could get. . .there.  Like if they came in from recess they were in.  You know if they were just finished a book then and they were tired it gave them a chance to zero in on where they were at and it made sense to me to differentiate the time for mathematics from the rest of the day and students hunger to do arithmetic ya know to do numbers ya know and uh satisfy them with a little bit of that. And so I saw it work at a school site and I would’ve felt dishonest if I had done what I didn’t think would work.

Many of the early Eureka writers were trained in elementary math teaching methods by Dr. Sagher and/or Robin Ramos.  Those who had the privilege to learn from these legendary trainers understood the depth and nuance that Sprints possessed.  We also knew that this power was only realized when teachers put great intentionality into their preparation and distribution.   When haphazardly selected and/or flippantly delivered, Sprints can easily become just another drill and kill speed routine or, worse yet, a frustrating problem set that students will dread.

Pendulum Transition

The camera zooms in on a few students whose pencils are gliding effortlessly down the first column.

Video Audio (Lead on paper)

They’re answering deliberately sequenced problem pairs addressing a common student confusion - 3 x 2, 3-squared, 4 x 2, 4-squared, 5 x 2, 5-squared.  The sequence then reverses - 6-squared, 6 x 2, 7-squared, 7 x 2.  Seeing their twitching wrists pulsating with adrenaline, you assume that these students have an internal voice calling out,  “Faster, Faster, Faster.”

You might find their quiet persistence to be a refreshing respite from 21st century schooling.  In a highly distractible world, saturated by artificial noises, the pitter patter of lead tapping paper evokes nostalgia for a past era when students more easily lost themselves in silent tasks.  Or, you might interpret the students’ diligence as fearful obedience.  They’re intimidated and work hard to not fall out of favor with me.

I can’t be sure, but I doubt the latter is true.  I taught many of these students’ older siblings and had known them since they were in kindergarten.

They might have wanted to please me and therefore tried extra hard, but I’m positive that this level of concentration and energy couldn’t be postured for a guest teacher.  Instead, it was a credit to the coherency of the school’s math program.  At Philadelphia’s FACTS Charter School where this was filmed, every first through sixth grade lesson began with a Sprint.  Prior to filming the video, the students had already experienced the routine close to 700 times.

Robin Ramos:  To keep something systemically patterned so that it’s an expectation of a routine is helpful because there’s so much disjunction between grade levels.  Students end up in classrooms that have completely different pedagogical approaches and it’s disorienting.  So even if the teacher delivers sprints in different ways at least there’s a basic structure and an essential element of the mathematics class that is carried forward and allows a student to bridge more readily.

I would have regrets if those students felt intimidated by me, but if their efforts reflected a desire to practice and improve, then I feel their internal pressure was healthy in the same way that they might feel a sense of accomplishment running a mile in under seven minutes or playing an instrument in sync with their favorite artist.

Regardless of how you perceive the video’s intense dynamic, I welcome your criticism.  It’s fair for you to believe that focused independent paper and pencil practice has no place in a 21st century classroom.  It’s also reasonable to think that what is gained doesn’t warrant the time needed to attain it and that the same fluency advancements could be achieved without using Sprints.  You can describe my demeanor as authoritative or even carceral, and not want your students or children to take Sprints, but please please please do not characterize the activity as a timed test.

Yes, I am holding a stopwatch, timing the students  to work for one minute, and yes I want them to correctly answer as many problems as they can during that time frame.  But – none of the Sprints will be graded or even seen by anyone other than the individual taking it.  Far from an assessment, this Sprint is a celebration of what the fifth graders have been learning.

Lauren Schauer:  Once they learn a new strategy, I’ll give them a Sprint. . .it’s not timed or anything.  It’s just that worksheet . . .and it matches the strategy that we did during that lesson.

That’s Lauren Schauer, an outstanding third grade teacher at Valley Charter School in North Hills, CA.  She’s taught there for her entire eleven year-career and starts every math lesson with a Sprint.

Lauren Schauer:  So they’re doing the Sprint for independent practice and then maybe the next day I’ll send it home for homework.  And then the following day it’ll be their Sprint during fluency time.  So they’ve seen this Sprint twice at least before doing it as an actual timed Sprint.

Fifteen years as an elementary math teacher trainer has led me to conclude - the most under-communicated tenant of Sprint delivery is that it’s only a powerful tool if students have already mastered the topic on the page.  Sprints are meant to reflect concepts that students have been learning.  Once mastered, the teacher uses it as a tool to help enter the concept into long term memory.  This doesn’t happen when teachers present them to students who still have a shaky understanding of their content.

A hard Sprint, therefore, is an oxymoron because a child who is confused or frustrated by it is really not taking a Sprint.  When this happens, the teacher made a poor selection and would’ve been better off picking a different topic that would’ve allowed all children to feel successful or not delivered one at all.

Dr. Yoram Sagher: You don’t learn during a Sprint.  You internalize and reinforce what you already know.

So why has this message been lost?  I assume that it’s because of the nature in which Sprints were introduced to parent, student, and educational communities.  The advent of the Common Core and Eureka Math’s subsequent implementation efforts often emanated from urgent turn key trainings.  Sprints were a tiny fraction of an enormous amount of information that district representatives were expected to quickly absorb.  As a result, they were tasked with attempting to train other teachers in its theory and delivery without first developing a deep understanding of their own.

In his 2006 workshops, Dr. Sagher spent two days exclusively training the theory, writing, and delivery of Sprints.  My colleagues and I spent hours in front of a computer creating Sprints and then practiced delivering them to each other in front of Dr. Sagher.  He critiqued the problem sets we created as well as our delivery of the routine.  The process was arduous and frustrating but we entered the school year with a firm grasp of what the tool was trying to accomplish and how we could maximize its use.

Delivering Sprints without first understanding their purpose and each stage of its delivery can at best create the optics of superficial enthusiasm.  At worst, it leads to dysfunction and student misery.

Pendulum Transition

Four days before the video was filmed, the students were introduced to exponents.  This started with the concrete - finding the area of different-size paper squares and connecting it to base/exponent notation.  The area of a 5-inch by 5-inch square, e.g. can be found by multiplying 5-inches by 5-inches.  For the previous 3 years, they answered questions like this by seeing and writing the digit 5 then the times symbol and the digit 5 again, but now they’re solving the same problem with a 5 raised to the second power.

In the three days between the exponent introduction and the Sprint, their teacher addressed a common pitfall that upper elementary students encounter during their early work with exponents - multiplying the base by 2 instead of by itself.  Not wanting their students to generalize a misconception such as 5-squared is the same as 5 times 2, the teacher decided to address it in the days that followed the introductory exponent lesson, using two- to three-minute whiteboard exchanges and call-response fluency drills.

Through intentional sequences and crisp delivery, they arrested student forgetting. Progress was initially slow, but by the end of the class’ fluency block the day before the video was taken, their teacher determined that the students had mastered the content & were ready to further commit it to memory.  Doing so while getting extra practice with times tables was a fringe benefit.

I’ve found that the most successful Sprint deliverers approach their fluency blocks like an athletic coach or music instructor.  In the days leading up to a performance, they target specific skills to practice in isolation.  By breaking big ideas into manageable chunks, they prepare their pupils to later execute at a more complex level.

Pendulum Transition

As the video inches towards the one-minute mark, the camera zooms out and you see all 25 students deeply focused on the problem set in front of them.

A handful of the children function two or three grade levels behind, but they are all working in a state of cognitive flow.  Most educators would agree that the latter is positive, but many hold reservations about the simulated Math race, specifically the timed component.

Some critics say that it sends students the wrong message about what Math is, i.e. an inappropriate emphasis on calculating speed.  I will address this later, but for now, let’s examine Dr. Sagher’s intention.

Dr. Yoram Sagher:  Adrenaline increases memory by a factor of 6.  It is a drug and the amusement park industry is founded on children’s love of it.  In other countries, teachers use a very destructive method to help their students learn basic math facts.  They put 100 problems on a page and position a large man behind them.  As students do problems, the man pressures them by saying Faster, Faster, Faster.  This of course will lead students to hate math.  The dynamic changes when children are prepared for the work and excited to show off what they know.  When the child is telling themself Faster Faster Faster the experience brings them the same joy as a roller coaster.

To stimulate this adrenaline, Dr. Sagher aimed to create a Math Race which would feel like recess in the classroom.  He recommended two pieces of theater that would further excite students.

Dr. Yoram Sagher:   Wear a baseball hat and hold a stopwatch.

Dr. Sagher’s opinions & conclusions can certainly be disputed, but dwelling on the activity theatrics deflects from their intended purpose.

Wearing a hat, holding a stopwatch, and beginning the routine with On your mark, get set, GO! are all attempts to generate energy and focus.  Some students respond well to this stimulus, others do not.  I believe that student interest & enthusiasm towards different school activities is less predicated on the actual activity than it is the spirit of the teacher delivering it.  Many educators can remember feeling anxious in school, possibly during timed math tests.  What they fail to account for is that their displeasure stemmed not from the stopwatch, but instead the person holding it.

The choice of how to begin the routine and whether or not to time the activity is left to the teacher’s discretion.  Not every teacher can look convincing dressed up as a coach, but everyone can facilitate quiet, focused practice with or without race theatrics.  Nothing is wrong with teachers beginning a Sprint routine by calmly saying Begin or Try your Best.  The aim is not solving problems at lightning speed, but instead quiet, focused practice in which the students are feeling successful.

Lauren Schauer:  You know there are extreme cases where students are really struggling with that timed pressure.  And so I’ll have like you know individual conversations with that particular student and explain the purpose of the sprint and that we want to embrace that like heart like that heart rate going fast. That’s uncomfortable sometimes.  We wanna embrace that.  That’s what’s going to help us grow and get better.

Students never have & never will hear me say that if they answer a lot of problems quickly, then they’re good mathematicians, nor will they ever hear me say that they’re not good at the subject if they’re slow in retrieving facts.  What they WILL hear is that aspects of the subject will come easier to them if they improve their number sense & don’t need to use a lot of working memory on arithmetic.  This ranges from knowing the commutative property of addition in first grade to times tables in third, & fraction operations in fifth.

My overarching message when initiating this activity has always been that everyone try their best.  This is no different than when they diagram word problems a few minutes after taking the Sprint or engage with independent practice following the lesson.  The message also doesn’t change later in the day when they participate in a Reading lesson, conduct a Science experiment, work on an art project, or play a kickball game at recess.

There is much in life that individuals can’t control, but effort isn’t one of them.  In all things, trying your best must be a constant.

Pendulum Transition

Many educators feel uneasy seeing 25 students hunched over a sheet of math problems working vigorously to answer as many problems as they can before hearing their teacher say “Stop!”  From where do these feelings emanate?. . .I can’t be sure but I assume a big part of it stems from their own school experiences.

Mrs. Johnson, my fourth grade teacher, gave a weekly timed math test with 100 computational facts on a page.  Anyone who answered them all correctly in one minute received a piece of candy.  Students who succeeded undoubtedly loved the timed tests and the rewards that came with it, but those who struggled surely did not.  Although I believe Mrs. Johnson was well-intentioned, I don’t endorse her practice.  This might seem strange coming from an unapologetic Sprint advocate, who isn’t adverse to classroom competition, but I see Mrs. Johnson’s fluency choice as drastically different than Sprints.  Both are pencil/paper activities in which students work intensively on math problems, but for the most part the similarities end there.  Prior to timed tests, Mrs. Johnson encouraged us to memorize a set of facts and then presented us with a randomized computer-generated problem set.

Cassy Turner:  The goal behind a Sprint is to focus on a strategy and calculate quickly that way.

Cassy Turner, Singapore Math Expert, Published curriculum writer, Trained by Dr. Sagher.

Cassy Turner: So once you have a strategy, having students do something like a Sprint is ABSOLUTELY fine because going from I understand the Math to I’m efficient and fluent with the Math - That’s your leap and the only way to get there is repetition.

Whenever I’ve seen Sprints fail, it’s invariably because the teacher has not drawn the connection between lessons, follow-up fluency activities, and the Sprint.  Conversely, Sprints that are run well feel like the culmination of what students have been practicing in class.

The Exponent Sprint seen in the video reflects a lesson and the ensuing fluency drills that accompanied it.  During our prep the day before the video was filmed, the homeroom teacher and I carefully examined the initial sequence with one slow processing student in mind.  Knowing that Diyah struggled with his times tables and confidence, we made sure that the first several problems would feel simple enough for him to bypass his unhelpful fear of failure.  We knew that if we could accomplish this for Diyah, then every other students’ affective filter would also be lowered.

Later in the day, right before dismissal, the teacher took Diyah aside and told him that they noticed how hard he was trying and that they badly wanted him to succeed.  They then handed him the Exponent Sprint and said, “This is tomorrow’s Sprint.  If you want, practice it tonight.  Just make sure that it stays at home, so no one else sees it.”  This simple gesture showed Diyah that his teacher recognized his efforts and was invested in his learning.  Oftentimes, this is enough to keep children from feeling anxious or discouraged.

As a sixth grade teacher, I heeded Dr. Sagher’s suggestion of always leaving the next day’s Sprint on a table in the back of the classroom.  All students knew that they were welcomed to take it home & practice for the next day.  Was this fair?

Dr. Yoram Sagher:  Why not?  The worst thing that can happen is that a child will memorize 88 problems.

The homeroom teacher and I also discussed Natalie, who functioned well above grade level.  Not wanting her to feel under-challenged by completing the Sprint in under one minute, we added some rigorous problems in the second column that required her to calculate cubes, double-digit squares, and single-digit numbers raised to the fourth, fifth, and sixth powers.

In the end, the problem set possessed a balance of simplicity and rigor, allowing every child to feel successful but also challenged.

Pendulum Transition

I had five years of teaching experience when I met Dr. Sagher, but had never been an elementary school math teacher.  With no pre-established philosophies or habits, I had little choice but to follow his advice.  I had no idea how to begin or get through a one-hour math block without delivering Sprints, so constantly refining and evolving the tool sprung more out of necessity than anything else.

During my early years of writing and delivering Sprints, I encountered many implementation challenges, most of which centered around the problem sets being too hard or easy.  To address the latter, I toyed around with different strategies to manage the routine when students finished early.  I tried having them record their time after they finished the last problem and even challenged them to start ten or fifteen seconds after I said “Go!”, but nothing worked well.  Dr. Sagher observed me try one of these methods and quickly dismissed my ideas.

Dr. Yoram Sagher:  Everyone must work for one minute.  If a Sprint is too easy for some students, rewrite the last ten questions so they cannot finish it the next time they take it.  Everyone must feel like they have the chance to improve.

I followed his advice and also created a precautionary measure to safeguard against early finishers.  In the corner of my chalkboard, I permanently displayed a “count by”, and told my class that, should they finish the problem set early, skip count on the back of the page until they hear me say “Stop.”

After two years of delivering Sprints daily, I concluded that the tool was working magnificently for 90% of my students. Unfortunately, the remaining ten percent were the children who most needed to improve their fluency. Entering my third year of teaching Math, I made it my year-long professional growth goal to change this. I wanted Sprints to work well for every student, including Jennifer - a child with an IQ in the eighties.

Although Jennifer was in sixth grade, her mathematical skill set was that of a first grader. She hadn’t automatized any of her times tables and struggled with simple addition and subtraction calculations.

For the previous two years, I had always rewritten Sprints whenever a student finished in under one minute. I simply replaced the last five to ten problems with more challenging ones, so that no one would be able to finish the next time I gave it. Fluent students seemed to respond well to the advanced rigor, trying harder when they felt challenged by the Sprint.

I realized that to engage my struggling students, I would need to inverse my philosophy for the first ten to 15 problems.  I started stealing glances at Jennifer’s Sprint scores.  If she didn’t get at least 11 correct, - one every five and a half seconds - I rewrote the first dozen or so problems, making them easier. This forced me to think critically about the initial sequence and calculation complexity of each Sprint. I found this exercise tedious and challenging, but also very rewarding. By the middle of the school year, all students were feeling successful and challenged daily.

Having accomplished my goal, I found greater joy – and art – in writing new sprints moving forward.  I have come to view the 44 problems in my blank Sprint templates in four quadrants.  I’ve asked Ashley Boyle, a second grade Washington D.C. public school school teacher to read their descriptors.

Ashley Boyle: Quadrant one. Problems below grade level. Each child should gain confidence by completing all the problems correctly in under one minute.

I don’t think that these problems can be “too easy.”

Ashley Boyle: Quadrant two.  Harder problems than the first quadrant, but still very easy.

These problems often address grade level concepts with the simplest possible computation and/or deliberate patterns and sequences.

Ashley Boyle: Quadrant three. Slightly harder computation and/or more randomized problem sets are introduced.  Problems incorporate grade level skills and complexities that all students have seen.

The rapidity of answering questions in this section normally slows down.

Ashley Boyle: Quadrant four.  Problems consist of more difficult computation and present challenges that the students have the skill to answer, but might not have been prepared for.

As students work through the four quadrants, they encounter variations and challenges that stretch, without overstretching, their skill set.  A ski slalom, therefore, is probably a better metaphor for the activity than a Sprint.  An initial energy thrust through the easy problems creates momentum for navigating twists and turns of complexity in the latter quadrants.

I always found the classroom atmosphere most dynamic when everyone got between 16 and 34 correct.  These informal benchmarks seemed like a vibrant balance of success and rigor.

Because of this careful consideration, Sprints fall into an elusive training category called Purposeful Practice, a term coined by late Swedish Psychologist Anders Ericcson in his acclaimed book Peak:  Secrets from the New Science of Expertise.  Here’s an excerpt from his audio book.

Anders Ericcson:  Purposeful practice has several characteristics that set it apart from what we might call, Naive Practice, which is essentially just doing something repeatedly and expecting that the repetition alone will improve one’s performance.

Just past the one minute mark, I say “Stop” and immediately begin calling out answers so that students can check their work.  They cross out or circle each answer they get wrong.  For each problem they answer correctly, they make a check mark and respond in the affirmative.

Video Audio (Students saying “Yes” as I call out answers.)

At no point during the 11-minute video do the students seem more robotic.  A Sprint detractor might call them little soldiers in their teacher’s infantry or - worse yet - liken the entire dynamic to a cult.  Their criticism might grow at the 1:20 mark when one student appears to throw their pencil down in frustration.  Those who already have their minds made up about what they’re seeing can’t possibly be swayed otherwise, but I invite the genuine skeptic to delve into the particular and consider the value and practicality of engaging in this call-response, even if they might feel uneasy about the way it is packaged.

Anders Ericcson:  Purposeful practice involves feedback.  You have to know whether you’re doing something right and if not, how you’re going wrong.

Students could of course check their work without saying “Yes”, but there was great intentionality behind Dr. Sagher wanting them to do so.

Dr. Yoram Sagher:  Children love to talk and show off what they know.  Having them say ‘Yes’ when they get an answer right allows them to do both.

There are two other reasons for students to verbally respond while the teacher calls out answers.  One is mathematical, the other practical.  By having the students check their work, they are able to immediately document their success or lack thereof.  While checking answers on the exponent Sprint, each child quickly recognized whether or not they were reading and computing exponent notation correctly, e.g. not mistaking 9-squared as the same as 9 x 2.  The girl who threw her pencil made this mistake and was no doubt frustrated with her own forgetting.

No teacher enjoys seeing their students angry, but it would be irresponsible to let misunderstandings continue without redirecting them to practice correctly.  The longer that students work without corrective feedback, the more likely they are to internalize a misconception.

Sarah Cottingham:  If you’ve got a misconception, it’s kind of a faulty way of thinking about something.  That that’s quite difficult to change and get rid of.

That’s Sarah Cottingham, a UK teacher trainer with an MA in Educational Neuroscience.

Sarah Cottingham:  Our brains are spotting something and think ‘Oh that’s similar to something I already know, but the thing they already know isn’t quite right. So then they kind of applying the wrong thinking in lots of scenarios.

The auditory “Yes” also cues the teacher to know when it’s no longer necessary to call out answers.

Video Audio (Students saying “Yes”.)

Many students sit idly as a few of their classmates continue calling out “Yes."  I always encouraged my students to record the number they got correct after I crossed the last problem they answered, and then immediately begin practicing problems they didn’t get to.

This is followed by the most controversial stage of the Sprint routine.  Students record how many they answered correctly and raise their hands.  In this clip, I provide plenty of ammunition for my critics who liken me to a drill sergeant.

Video Audio (“Hand High, Elbow Straight”)

Students know to raise their hands if they answered one or more correctly and to drop their hand when I cross their number.

Video Audio (“Two, three, four, five. . .”)

I then recognize the students who answered the most correctly, awarding 1, 2, and 3 claps for the third, second, and first place finishers, respectively.

Video Audio (Recognize winners)

This stage of the routine can understandably be interpreted as celebrating speed.

But again, let’s delve into the particular.  The reason I recognized winners was to stimulate a collective focus.  Children are competing for one, two, or three claps and the peer recognition that comes with it.  My intent was less to celebrate speed, and more to create another piece of theater.  By competing for recognition, I raised the activity’s stakes, hoping to stimulate a greater effort in the process.

Anders Ericsson:  Purposeful practice is focused.  You seldom improve much without giving the task your full attention.

Consider a friendly game of  poker or pickup basketball in which the players don’t gamble or keep score, respectively.  Participants tend to be inattentive, play becomes sloppy, and everyone quickly loses interest.  But, put a quarter in the middle of the card table or determine that the first team to score 11 points wins, and collective energy increases, usually improving the quality of play.

I never felt that my students became dejected when they answered less problems correctly than their classmates.  More often, I found that it brought out the best in every students’ efforts and character.  It never even crossed my mind as something to consider not doing until I introduced Sprints in a professional development the summer after the video was filmed.  Some teachers disregarded the entire tool and routine solely on the basis of clapping for winners.

As Eureka Math rolled out Sprints, the pushback increased.

Robin Ramos:  The bubblewrap baby thing was already something I had kind of a judgment of so when that feedback came in I felt it was from the bubblewrap crowd as opposed to people who wanted their children to succeed and you know weren’t going to cringe every time they had what they thought was an unpleasant experience.

As a teacher, I always enjoyed holding classroom competitions despite the symptomatic challenges that inevitably arose.  Through Sprints and other contests, I felt like I was able to teach my students valuable life lessons, such as succeeding with humility, struggling with dignity, and always trying your hardest regardless of the challenge or one’s feelings towards it.   There were of course times when feelings were hurt but in the end, I felt like the benefits overwhelmingly outweighed the negatives.  Duane Habecker agrees.

Duane Habecker:  On a cost benefit analysis, I think they do more good than harm.  It’s all about creating a winning proposition.

Weeds sprout in well-tended gardens and even great classroom activities possess foibles.

My response to skeptics who dislike recognizing winners is always this:  In the most extreme cases, a few students might never feel like they’re great at Sprints, but that isn’t a reason not to deliver them.  Classrooms are filled with amazing scientists, readers, writers, actors, artists, musicians, athletes, comics, and thinkers.  Any good elementary school teacher knows this and finds ways to regularly recognize each of their students’ special talents.  This makes children feel loved and when they feel loved by their teacher, they trust their decision making and embrace the activities that are presented to them.  Although we don’t want students to equate rapid retrieval of computational facts to mathematical success, there’s nothing wrong with acknowledging those who are good at it.

The most important aspect of this stage in the Sprint routine is that students are able to immediately assess their understanding.  Recognizing winners is the choice of the school and/or teacher.  An alternative to recognizing winners is asking students to raise their hand if they tried their best and then acknowledging their effort in whatever way they see fit.

But, regardless of the activity or subject being taught I would caution any teacher against aiming to avoid student uneasiness at any cost.  Children should never feel frightened at school, but they also shouldn’t pass their days in a perpetual state of ease.  No person - young or old - can reach their potential if they don’t get out of their comfort zone.  More from Anders Ericcson.

Anders Ericsson:  Getting out of your comfort zone means trying to do something that you couldn’t do before.  This is a fundamental truth about any sort of practice.  If you never push yourself beyond your comfort zone, you will never improve.

Jason Ablin, author of The Gender Equation in Schools put it a little differently.

Jason Ablin:  A calm stress is the best state to be in to allow students’ executive functioning to flourish.

For the next two minutes, students quietly work on Sprint A problems that they didn’t yet complete.  There is an atmosphere of quiet diligence but the collective energy is more relaxed.  A few early finishers help me distribute papers and others are free to use the time however they choose.  Some count by twelves in the margin of their Sprint and others sit idly.  Around the 3 min 40 sec mark I help a student who’s struggling with a problem.  Depending on the day, I might also use this quiet practice time to distribute materials for the lesson that follows.

Lauren Schauer uses the short practice session differently,

Lauren Schauer:  That time in between side A and side B.  That’s the time where they can share out strategies and like patterns that they noticed..when they were doing side A so that they can you know help each other to be faster on side B.  And so most students are usually excited to share because I’ll write their strategy on the board and like name it.  ‘Like oh this is Joey’s strategy.  Who’s going to use Joey’s strategy?’ and then they’re kind of like eager to share their strategies.  And then it gives the rest of the class the chance to hear something that actually might help them be faster on side B and build their confidence. . .They’re turning and talking, noticing patterns, writing things up on the board.  Trying to give them something quick so that when they do side B they have something to help them go faster.

Of the several hundred times I’ve observed a teacher deliver Sprints, this between A and B time is by far and away the most neglected stage.  Too often, teachers begin by directing their students to work for one minute, call out answers, have them record their scores, and then immediately begin Sprint B.

Children desperately need this quiet time to reflect, correct mistakes, and practice harder problems.  All the while they know, if they take this practice time seriously, they’re likely to improve their score on Sprint B.  The early finishers who are counting by twelves are also gearing up for a second race, knowing that if they can complete all 44 problems in under one minute, they don’t stop working, but instead write out multiples of twelve until they hear me say “Stop.”

The most successful Sprint deliverers create a rhythmic ebb and flow to their routine in which short bursts of energy punctuate periods of calm practice.

Video Audio: If you’re not quite done yet that’s fine. . .Put your finger on number one. . .Ready.

I again review Sprint A and students say “Yes” for problems they answered correctly.  At the time, I had never experimented with different ways of involving students in this stage so the call-response was always fairly monotonous. But after observing a great fourth grade teacher in Los Angeles, I came away with new ideas to make it more engaging.  Rachelle Bertumen, who now works as a Eureka Math Professional Development Implementation Specialist, maintained student focus by mixing up who called out answers.

Rachelle Bertumen Voice Over

This stage is meant to help student confidence, because they’re getting immediate confirmation on how well they practiced during the two-minute work session.

At the 5:14 mark, all students are standing.  The girl who threw her pencil can be seen hopping in place and throwing air punches, eagerly anticipating the upcoming exercise.  Her frustrations appear to be forgotten.

Some of the students have been sitting for nearly five minutes and are happy for the stretch break.  This pleases me, but there’s also an academic reason for getting them out of their seats and moving.

Dr. Yoram Sagher:  Kinesthetic memory is strong memory.  Counting forward and backward by a multiple while doing a fast-paced exercise helps students internalize number facts.

The quiet practice session following Sprint A creates a collective energy lull.  This stage of the routine reinvigorates student focus while helping them temporarily forget about exponents, which have consumed their mental energies up to this point.

Video Audio: (“Friday is Punch Day.”)

Rapidly, we punch the air, simultaneously counting by nines in unison.

Video Audio: (Counting by nines)

Fast exercises are followed by a slower one in which the students again perform a count-by, often by a more challenging multiple than the one used in the first exercise.  In the video, the students and I do slow arm circles while reciting eights.

Video Audio: (Counting by eights)

This allows them more think-time as they count, slowing their heart rate in the process.  It is a period of calm that helps them approach Sprint B with renewed effort and energy.

How the remaining time of this stage is spent varies greatly from classroom to classroom.  Some teachers only do a fast and slow exercise.  Others deliver call-response and/or whiteboard exchange fluency drills.

In the video, I direct students to hum-count sixes forward and backward, a stepping stone to count units of twelve later in the school year.

Video Audio: (Hum/Talk sixes)

In total, there is a three-minute stretch break that serves the same purpose as halftime of an athletic contest or intermission of a play.  The performers get a mental break from the event and will return to work refreshed and focused.

Pendulum Transition

By the 7:48 mark, the students have returned to their seats, ready for their second race.  Most, if not all students, quickly glance at their A score, giving themselves a target to pass in the next minute.

Anders Ericsson:  Purposeful practice has well-defined, specific goals.

Regardless of the grade or subject they teach, good teachers emphasize that Personal best is success.  Teachers who deliver Sprints well help their students understand that their aim should always be improving on their first score.

Lauren Schauer:  . . .and while we do like simulate a race, the focus is always on the improvement that they personally make between side A and side B and so that’s what we’ll like celebrate.

Let it rip!

Video Audio: (“On your mark, get set, Go!”)

The whoosh is louder this time.  Lead scrapes are intenser and inner voices more urgently prod Faster Faster Faster.

Deeply wired within the human psyche is a longing to realize one’s potential.  This latent desire has been aroused.  Everyone wants to beat their first score and in the back of many students’ minds lies the prospect of earning Most Improved of the Day.  

The Sprint B procedure is nearly identical to Sprint A.  I say “Stop” after one minute and immediately begin calling out answers at which time students say “Yes” if they get them right.  My delivery is fairly bland.

Video Audio: (”YES YES”)

Now, listen to the way Rachelle infuses rhythm and concentration into this stage.

Rachelle Bertumen Voice Over

At the 9:52 mark you can hear me deliver the last answer - 216.  This time, a few students finish every problem on the page, so when I hear an affirmative answer, I immediately start skip counting by twelves, maintaining the same call-response rhythm.  It’s not visible in the video, but the number 12 is circled in the top right corner of the chalkboard.  All students know that they are never finished working until they hear their teacher say “Stop!”

Video Audio: (Calling out answers and recognizing winners.)

As I was calling out answers, Students recorded their Sprint B score and calculated how much they improved by.  I then repeated the process of recognizing Sprint B winners before shifting focus to improvement, asking the students to raise their hand if they improved by one or more.

Video Audio: (Recognizing Chi)

Chi is the same student who threw her pencil in frustration.  Sprint B offered her the opportunity to redeem her struggle from Sprint A.

Duane Habecker:  When they are operating under a constraint of time, looking for the patterns.  What patterns are you seeing in this very carefully selected sequence of problems?  What are you seeing?  How can you make use of this pattern that is developing fluency and then measuring between an A and a B, recognizing and admiring and acknowledging and celebrating the positive effects of me getting better at fluency.  ‘Look at this!’

To know for sure that the improvement was authentic we need to examine the structure of Sprints A and B.

Number one on Sprint A is 2 x 2 and number one on Sprint B is 5 x 2.  These equations are roughly equal in difficulty.  2 x 2 and 5 x 2 are followed by two-squared and five-squared, respectively.  And so it goes.  Problem by problem each equation in Sprint A is analogous to the corresponding equation in Sprint B.

Students might not know how intentional the design is, but they’re well aware that when they do better on Sprint B, they have a feeling of sincere improvement.

The evening after the video was filmed the classroom teacher and I edited the last ten problems of the Sprint, including extra challenging problems such as 4-cubed plus 4-squared and 10-squared minus 8-squared.  We did this because we knew that two weeks later, the students would be taking the Sprint again.

Robin Ramos:  One thing I would do if I were gonna do it again. . .again, based on my own experience.  I thought that the Sprints changed too much.  So, I think I would rotate Sprints and use the same ones over and over again.  From my experience, I thought that having a new Sprint all the time is disorienting for students. . .maybe choosing 30 for the year - essential Sprints, and just rotating through them and let students see themselves improve with a single Sprint.  Not doing them so much that they would memorize them ya know they would go ‘Oh. This is this Sprint’, but enough so that they’re familiar.

As a sixth grade teacher, I always met with the fifth grade teachers towards the end of the school year to familiarize myself with the students I would be teaching in the fall.  Then, over the summer, I carefully selected the first ten Sprints of the school year, addressing topics that I knew every child would feel successful doing.  This often involved simple addition and subtraction topics on a first or second grade level or an easy terminology such as finding the Mode of a short list of numbers.

My reason for doing this was simply to help students create a success association with the Sprint routine.  During my 20 years working in education, I’ve found that very very few students don’t arrive on the first day of school with a good attitude, giving their teachers an opportunity to hook them into their classroom culture.  I’ve also found that this window can quickly close and a frustrating math experience often accelerates a child’s negative mindset towards the subject and school at large.

Because this current is challenging to redirect, I wanted the first two weeks of math class to be one of overwhelming success.  This bought me time to develop relationships with students and, once I earned their trust, I found them more resilient if, later in the year, I gave them a Sprint that was a little hard.

Lauren Schauer:  Like, we’ll address those kinds of things at the beginning of the year and spend those first few weeks of school establishing the Sprint routine and the expectations and help them understand that idea of racing against yourself. 

Once I chose ten Sprints, I cycled through them for the remainder of the school year, occasionally inserting new topics that addressed grade level learning.  As the list of Sprints grew larger, I gradually phased out the simple ones that I used to start the school year.  By January or February, I had a robust collection of 20-25 Sprints, many of which served as cumulative reviews for the remainder of the school year.

Eureka Math Squared is my favorite elementary math curriculum.  Many of the greatest educators I’ve ever known were, and/or remain, on their writing team.  Still, I think the company made a critical mistake in how they chose to incorporate Sprints in the curriculum.  By aligning them with individual lessons, Eureka accidentally set up the tool for widespread failure.

Elementary school educators often feel uncomfortable teaching math and fall into the habit of blindly following company lesson scripts to guide their instruction.  Lacking the confidence to question textbook authors, teachers often delivered Sprints that the curriculum recommended, even if they knew their students were collectively unprepared to succeed on it.  This led to frustrated children and in time many teachers, understandably abandoned the activity.

As a Eureka fluency writer and author of most of the curriculum’s Sprints, I should’ve suggested a better way to present them.  Creating a Sprint database organized by topic, might have empowered teachers in ways that aligning them to individual lessons and grade levels could not.  With access to hundreds of topics spanning multiple grade levels, teachers could have selected Sprints that better targeted their students’ fluency needs.  This would’ve led teachers to take greater ownership of their lessons, resulting in better student outcomes.

Pendulum Transition

The conclusion of the Sprint routine is punctuated more by what doesn’t happen than what the students are doing.  Unlike the A Sprint, I don’t provide additional time for students to practice problems they didn’t get to on Sprint B.  The event is over and more work with Exponents would feel excessive and counterproductive.  If the students and I both gave our best efforts, then we are tired and it’s time to move on to a different stage of the class period.

Everyone knows that they’re welcome to stow their Sprints away in a Math folder and later, if they want, practice problems they didn’t complete.  Those who don’t want to keep the Sprints know to place them in a scrap paper tray or recycling bin.

One option that no student has is turning them in to their teacher.  This is because doing so would shift the entire mentality of the activity.  The moment an educator collects student work, they increase the likelihood of individuals feeling assessed and/or analyzed. When teachers collect Sprints they risk changing the activity’s psychological dynamic from fun and invigorating to stressful and laborious.  

Pendulum Transition

At 11:01, I signal the filmer to stop recording and the video freezes, leaving you to make your own judgments about Sprints and my delivery of them.

It was filmed a quarter of my life ago so in many ways I too am left analyzing the same man that you are.  I now wear eyeglasses, my hair is a thinning salt and pepper mix, and my knowledge of children, school culture, and elementary math has expanded.  I’m not a new man, but I have evolved.

Was I a drill sergeant?  I prefer thinking of my younger self as a no-nonsense athletic coach - at times overzealous, but deeply invested in my students’ learning and making them each feel valued and cared for.  Back then, I felt - just as I do now - that different times of the school day called for different teacher personas, and I wanted the start of every math class to feel like recess in the classroom.

For those ten to fifteen minutes, I did everything I could to optimize student concentration and for better or worse stimulate healthy competition.  In addition, I wanted each child to be excited for Math class, while improving their conceptual and computational fluency.  For the five years leading up to filming the video, delivering a Sprint in the way that I did was the best way I knew to accomplish this.

I have few regrets.

This is because my memories of delivering Sprints are joyous ones.  I close my eyes and can see Michelle, En-Hui, Karon, and Suzanne, each of whom almost always won in their respective classes.  But these aren’t my most vivid recollections.  Instead, I remember Angeline’s proud smile the first time she correctly answered more problems than En-Hui, and Hanani high-fiving me when he improved his B score by over 15.

I also think of Onya, the only student I ever had who - for an entire year - kept every Sprint she participated in.  Onya was an average math student who rarely distinguished herself during the routine, but as a seventh grader, she created a portfolio to document her improvement over the course of the school year.  When it came time for her to apply to high schools, she brought the portfolio to her application interviews.  Today, she is a college graduate, supporting herself as an actress in Philadelphia.

But more than anyone, I think of Jennifer who underwent a personal transformation during sixth grade, in the process inspiring my four-quadrant approach to writing Sprints. Jennifer is the most behind grade level student I’ve ever taught.  In September, she entered the classroom sheepishly, shoulders sunken and pointing inward, trying to make herself invisible, but by the end of the school year, she arrived at her desk walking crisply and upright.

Once seated, she’d peer up at me, half-grinning, with her pencil gripped firmly, waiting for me to begin the routine, all the while knowing that she had little chance of answering more problems correctly than any of her classmates.  Jennifer’s motivation was strictly internal and she delighted in the rush she felt when whisking her pencil down the page, effortlessly answering problems she knew the answer to.  It was a feeling of academic success previously unknown to her, and during a late-year parent/teacher conference, her mother told me:

“For the first time in her life, Jennifer feels good about herself in school.”

It is easy to romanticize the past, and my lens is certainly biased, but I can’t recall a student who disliked Sprints.  Occasionally, I heard grumblings of “Not this again” but I always attributed it to the nature of middle school attitudes rather than a sincere aversion to the opening class activity.

My response to these complaints - which were few and far between - was always, “If you don’t want to participate, that’s fine.  You are welcome to just sit there or read a book while the rest of us have fun.”  In five years of delivering Sprints daily, I never had a child skip the routine more than twice, and I always felt that had I chosen a different way to begin class most or all of my students would’ve been disappointed.  Is it possible that some of them disliked starting every class period with a Math race?  I suppose, but if this was so, they did an amazing job of hiding it.

Still, eleven years of visiting different schools around the country has expanded my professional outlook, and I no longer regard the profession in as many absolutes as I did when the video was filmed.  I now realize that educational tools and their delivery are not universally powerful, and ways that educators effectively teach and communicate with students is not static.  Children’s nature might be timeless but their reaction to an ever changing society is not.  Only the stubborn and foolish deny this simple truth, and never consider changing their ways.

I no longer believe that Sprints are a magic bullet that can solve all students’ computational deficiencies, or that there aren’t other good ways of developing fluency.

But for now, I’ve seen Dr. Sagher’s invention do far too much good to see it as wrong or antiquated.

When I one day return to the classroom, Sprints will begin the first lesson I teach and - just as I did 16 years ago - I’ll go to great lengths to make it work.  Prior to initiating the routine, I might try to minimize its potential shock value by explaining their purpose to students and parents.  I also might change the activity name to Slaloms and/or not recognize winners, but I will keep the tool’s essence firmly intact.

This is because I believe that developing discipline, perseverance, and working stamina continue to be the most important characteristics of successful students and people.

I also think that elite mathematicians are our civilization’s only hope of averting disasters the next century promises to bring, and a generation of students with strong number sense is the best way to help produce them at scale.

But more than anything I’ve come to view Sprints as a metaphor for approaching life.  When learning a new skill or concept, humbly accept that challenges will arise and intensive practice provided by a mentor is the only way it will one day become simpler.  As you work, always try your hardest, but if you don’t reach your goals, understand that your personal best is success.

Those four things - learning, embracing challenges, practicing, and accepting the results of your best efforts - together fill human existence.