*Dave Reid is a high school mathematics teacher in his third year of teaching. He received his MA in Education and credential in secondary mathematics and physics from Stanford University in 2011. Dave spent a quarter of a century in high-tech primarily in the wireless and Global Positioning System (GPS) industries. He earned a BS degree in electrical engineering from George Mason University, and an MBA in finance and marketing from Santa Clara University. He also attended the U.S. Military Academy at West Point. He blogs as Mr. Math Teacher and tweets as @mathequality.
*

**Holding students to high expectations is not just for teachers**.

As I counted off students in my fourth period Advanced Placement Calculus class recently, I came up one person short. My immediate thought, before I even knew who was absent, was that I hope the student does not fall too far behind, as we switched to a modified block schedule for this academic year; missing one day puts a student nearly two instructional days behind.

In a demanding course such as AP Calculus, many students reel from learning that they are not as naturally gifted in mathematics as they may have come to believe given their nearly stellar performance in earlier mathematics coursework. AP Calculus shakes the foundations of even the most mathematically gifted of students, while those that are not as gifted can be downright fearful….

By the end of the second week of class, [senior] students who are highly unlikely to be able to handle the demands of the course have either dropped or decided not to take any mathematics course their [last] year…. Fortunately, with frequent encouragement and supplemental support from their teacher, remaining students are typically able to overcome the initial shock of the course and rise to its challenge. In fact, my two AP Calculus sections [are] now preparing to hunker down for the demanding nine months ahead of them….

So, it was with great apprehension earlier this morning that I … [scrolled] down the attendance roster to the end where students who have dropped are recorded, I confirmed, with great sadness, and a rising anger, that another student was permitted to drop my course. How could an administrator approve a student’s request this far into the course without contacting me for my perspective? Making matters worse, the prior Saturday morning I had notified the assistant principal of instruction, and the principal not to drop any more students from the course, as fifteen-percent of my original roster had already dropped. For whatever reason, my request went unheeded.

**The Class Must Go On**

For a few seconds I simmered with anger. However, allowing my emotions to overtake me would not accomplish anything, especially as I had dozens of students waiting for me to start the class…. After helping students connect, graphically and algebraically, what they learned about slope in algebra 1 as well as what they learned about secant and tangent lines in geometry and functions with the newly learned calculus concept of limits, the class worked on homework problems as I worked one-on-one with students who needed help. Fortunately, the focus required in the moment helped students learn a new concept well, while keeping my mind off of the frustration I felt earlier in the period. As the bell rang, I dismissed students reminding them of their upcoming test the day after the long weekend.

**Speaking My Truth**

After class was over, … my mind revisited the emotions I felt earlier in the morning when I learned that Espy [had] dropped my course. Anger turned to sadness as I reviewed [her] transcript and GPA. [She] has a 4.0 GPA with A+ grades for all of her prior mathematics coursework; additionally, she worked diligently to develop proficiency in English as her high California English Language Development Test scores revealed. All indications are that she is on the path to become a first-generation college graduate. I know what that journey is like, as I am one myself. However, English is my native language, not Espy’s. My wife knows all aspects of that path, as she is a first generation Mexican American, first generation college graduate, and English was not her first language….

As I required my incoming students to write about themselves and mathematics, I noted that Espy wrote that mathematics is her favorite subject in high school, yet she also knew she needed to keep up her strong study skills to do well in the course given its emphasis on conceptual understanding in addition to procedural fluency….

Yet, those words no longer carried significance for Espy, at least for my AP Calculus course. Feeling wholly dissatisfied with what happened, I took the time to compose and send the following email to the entire administrative staff of my school: four assistant principals and the principal. I … strongly believed that in their attempt to honor a student’s request, the administration inadvertently took away the student’s opportunity to experience a rigorous college level course.

My words to the administrative staff follow….

*I am very disappointed that Espy was dropped from my 4th period AP Calculus AB course without anyone consulting with me. While there are absolutely students who should drop the class, for a variety of reasons, Espy is not one of them….*

*Espy is the exact type of student this nation wants to succeed in an AP Calculus course. She may not know it herself, but she would have done extremely well in the course. She scored nearly ten percentage points above the mean score for all … students on my AP Calculus readiness test; she has the prerequisite skills to succeed in the course. She even has the potential to receive an A and pass the AP Exam, perhaps with a 4 or a 5.*

*If she had spoken with me, or an administrator had spoken with me, before dropping the course, I am confident I could have convinced her to stick it out, even if she felt overwhelmed at the time. I was able to do just that with another student, Ramon; he will do well in the course as well, as long as he holds up his end of the bargain, which is to spend time outside of the class period ensuring he learns the course material….
*

*I am still a very new teacher who does not know all the traditional norms and conventions about how a school operates. And, in general, I am not a letter of the law person but a spirit of the law person, which is why I am so disappointed in this situation.*

*I also know that whomever approved her request did so because they wish to support her, and help her. Yet, in my opinion, what happened is exactly the opposite of support when it comes to developing perseverance, building confidence, demonstrating the ability to challenge oneself, and maintaining proficiency with mathematics in their senior year.*

*Let me tell you how I handle similar situations in my algebra 1 classes. When I call on a student who may not know an answer, or may not even know that they can reason their way to the answer, an adjacent student often whispers the answer to them. When that happens, I immediately chastise the well-intentioned, but misguided student since they deprived the student I called upon from a critical learning experience. I explain to the “helpful” student that they, in fact, were not helpful. I make sure to tell them that I know that what they did was well-meant, however, paradoxically, it has the exact opposite effect. *

*This is a teachable moment for everyone. The lesson being that when we are immediately rescued from a challenging situation, we miss out on becoming stronger, developing confidence, and being able to recognize that we can, in fact, overcome adversity, even when we believe deep down inside that we cannot.*

*The reason I gave up my career in high tech where I made more than our superintendent, is not because I sought an easier job, afternoons or summers off, or to teach mathematics, or any particular subject for that matter. It is simply because I felt a calling to help students overcome challenges in their lives, and teaching mathematics is a conduit for that task….
*

*Unfortunately, over the past several decades, we have succeeded in convincing hundreds of millions of people that they are “not good at math,” when in fact, what is called math in most secondary schools is not even close to mathematics in all its splendid glory. *

*On the flip side, we have convinced tens of millions that they are good at math, when in fact, they are exceptional at memorizing, and succeeding in an … oversimplified, and direct-[instruction class]. However, when they face something slightly more complex … they fall apart as they have not developed the internal fortitude to persist with a problem that on the surface befuddles them. Our culture emphasizes finding a solution quickly, otherwise one might be perceived as weak or incompetent. This social norm compounds the perceived complexity of the problem for American students, leading most to give up prematurely, often commenting they have not yet been taught how to do this type of problem…. Research supports this latter point as students in Asia persist with a problem for minutes, or even tens of minutes before giving up, while students in the United States persist for tens of seconds, then give up. As a new AP Calculus teacher, I can readily attest to this phenomenon.*

*Hence, even our best and brightest are inadequately prepared for success in college, or beyond, as their problem solving … is more aptly described as working mathematical exercises than solving mathematical problems. This type of engagement with mathematics does not exist in our world outside of our classrooms…. No one is paid well to work mathematics exercises, yet that is how we prepare our most capable students, along with those who struggle mightily….
*

*I remain deeply saddened by Espy dropping my AP Calculus … course. I intend to speak with her to learn more about her request to drop the course. I hope it was not simply because she feared she would not be able to succeed in the course, or worse, that she might not get an A. She very well could receive an A in the course, and the only way she would fail would be to give up. I try not to let students give up on themselves. I cannot convince all of them, and there are some who I know may not have the best preparation to succeed in the course, so I accept their desire to drop. Espy is not in the latter segment of students.*

*I do not blame anyone here. I am upset, but I completely understand that what was done was believed to be in Espy’s best interest. I just do not believe that it truly is in her best interest, unless there are extenuating circumstances, of which I am ignorant. Even if that is the case, I could easily implement accommodations to support Espy in those circumstances…. This is how I believe we best help our students develop into their full potential.*

*Respectfully,*

*Dave*

*PS I know that many students complained that this course will be too difficult for them, that they do not want to work this hard in their senior year, or that I am not the type of teacher they wish to have in high school. I understand these perceptions. For some, I accept them, even though I believe the student is missing out on a grand opportunity to experience a rigorous learning experience that will benefit them immeasurably in college and in life. I purposefully portray the course as challenging, daunting even, as it truly is for many students given their preparation for this advanced course.*

*At the same time, I inform each and every student, repeatedly, that if they invest time outside of the class, using any or all of the many resources I provide to them, demonstrating their commitment to succeeding in the course, that they will succeed…. [I]f we allow students to give up on themselves too quickly, or fail to notify someone such as their teachers who truly know the student’s abilities as well as what they will face content wise so they can participate in the decision, we are falling far short of what I believe is our primary raison d’être as educators.*

**Reaching Out to Espy
**

A few minutes after sending my email message to my administrative team, I composed and sent a separate email message to Espy in hopes that she might reconsider her decision….

*Hi Espy.*

*I was saddened to see that you dropped AP Calculus.*

*I believe you have what it takes to pass this course, possibly with an A, and to pass the AP Exam with a 4 or possibly a 5. Your readiness test score was well above the average for the course. In fact, I was impressed with your scores on all of the topic areas. You are more than prepared for the rigor of this course in terms of prerequisite knowledge.*

*I understand you may feel overwhelmed with the challenge this course presents. It is daunting. However, you could, and still can, overcome the challenge, if you believe in yourself. I believe in you.*

*If there is anything I can do to make it possible for you to be reinstated in this course, to include special accommodations for you, please let me know. I am a very reasonable person, in spite of the “persona” I portray in the course. It is a “tough love” persona, akin to that of Jamie Escalante, from “Stand and Deliver.” I admire him greatly for what he was able to do for so many students who did not believe in themselves, or their academic abilities.*

*Espy, I want you to take this course. I believe it will be good for you. I know it will help you develop into a stronger, more confident, and likely more capable person. I hope you reconsider your request.*

*If I could find you easily, I would deliver this message face to face. However, I am unable to do so as expediently as sending this email.*

*Regardless of what you decide, it was great having you in my class. I enjoyed seeing you smile, even at my poor attempts at humor.*

*I wish you the best in all that you pursue.*

*Mr. Reid
*

**A Personal Delivery**

Even though I sent emails off to both the administrative staff, and Espy, I felt compelled to do more to ensure Espy received my request, and carefully considered the possibility of rejoining the class….

Towards that end, I dashed off to print out my email and hand-delivered it to her sixth period teacher. I briefed Espy’s teacher on the situation, asked her to read the letter, and to deliver it to Espy, hoping she might encourage Espy to reconsider. She willingly agreed. She actually did more than I anticipated.

**Epilogue**

Espy’s sixth period teacher not only delivered my message to Espy, she allowed another educator, who co-taught with her on occasion, to read it, as she was working to involve more female students in science, technology, engineering, and mathematics (“STEM”) programs and fields. With this fortunate coincidence, Espy had not one, but two additional advocates to discuss why she dropped, to encourage her to reconsider, and to follow up about her situation with on campus counselors.

The two teachers spoke with her at differing times sixth period letting me know afterwards that tears had welled-up in Espy’s eyes as they asked her what she planned to do. Tears nearly welled in mine when I learned of hers.

I have yet to hear from Espy. I hope that she rejoins the class. Only time will tell.

**(EDITOR’S NOTE: Dave Reid contacted me a few days later and said the following:**

“I sent another email to Espy relaying the fact that my wife is a 1st generation college grad and 1st gen[eration] Mexican American who took AP Calc in high school, passed and had a 4.0 GPA.

Espy sent a terse one sentence reply with no subject line thanking me for my concern but stating that she made a decision and was sticking to it….

So, no fairy tale ending here. But I gave it my best, and that’s all I can ask of myself or anyone.”

Well done Mr. Reid!

Larry, I really enjoy these vignettes from folks that are career-switchers to teaching, as I also am one. Keep them coming!

Thanks, John, for the comment.

Thank you for this thoughtful and on spot post: I wonder if Espy, or other students, would stick it out if those GPAs weren’t the “golden” tickets for admission to some elite college; I wonder if we set students up to behave the way they do? The work of Carol Dweck, her book Mindset is an great introduction, gives us some clues. So does the work of Albert Bandura, Social Cognitive Theory, and that of Ryan and Deci, Self-Determination Theory. When people are told they are smart and evidence of this “smartness” is based on grades — what happens when those people face a challenge and fail (they get a “B” instead of an “A+”)? We have to stop putting so much value on the grade, more on the discipline, persistence, and ultimate outcome that takes us from one point, whatever it is, to the next. In your post you note that Espy could have gotten an “A” — you know this is the prize. I think you are struggling not only to keep Espy, but to make your reason for becoming a teacher — which I so admire — jive with a system that is out of synch. I love your reflections, you help us all to do some important thinking, and I hope you can get more students to tackle the AP Calculus challenge.

Thanks, Sarah. Our educational system absolutely sets students up for a GPA gauntlet where they believe they must get straight A’s while taking ridiculous numbers of AP courses, participating in multiple varsity sports, serving in leadership positions at the school, and volunteering during weekends and summers, often far outside their community. Frankly, it is too much. Most elite colleges and universities feed this frenzy by implying that the only true path to a life worth living is through their hallowed halls, when many state universities are a much better value, with nowhere near the competitive craze. The College Board is not without blame in this game as well. I’d much rather simply teach calculus rather than AP Calculus. However, the College Board pitches a convincing value proposition: take these classes and possibly save money in college by graduating earlier. As the pass rate for the AP Calculus AB exam hovers around 50%, and even lower at 35% or so for a 4 or a 5, which most colleges require for credit on calculus I, the course becomes a crap shoot for many, especially those who struggle the most with mathematics. The College Board, perhaps as a sort of legal disclaimer for their broad, and somewhat misleading enticement for more students to take AP Calculus, provides the following disclaimer, which few students read, or even truly understand.

“Success in AP Calculus is closely tied to the preparation students have had in courses leading up to their AP courses.

Students should have demonstrated mastery of material from courses that are the equivalent of four full years of high school mathematics before attempting calculus. These courses should include the study of algebra, geometry, coordinate geometry and trigonometry, with the fourth year of study including advanced topics in algebra, trigonometry, analytic geometry and elementary functions.”

Students simply feel compelled to take the course given the deeply held belief that they must do so to distinguish themselves amongst the sea of applicants at elite institutions.

Yet, few students have mastered this material, especially the advanced topics, prior to taking AP Calculus. This deficiency becomes apparent immediately after they attempt to understand the first concept in the course: limits. And as they progress, they start to realize that the maxim “calculus is easy, it’s the algebra and the trigonometry required to complete the calculus that is hard” is quite true.

On the “Mindset” front, my first assignment of the year for all of my courses requires a student to learn about Carol Dweck’s work; see http://www.sophia.org/tutorials/mindset–2, which is the online assignment. Nearly all of my AP Calculus students responded that they have a growth mindset, when I believe our system has acculturated them into fixed mindsets with our obsessive focus on GPA; most students are simply too accustomed to getting A’s in decontextualized, procedurally focused mathematics courses, which do not adequately prepare them for the rigors of calculus. When students first experience this dilemma, whether in an AP course in high school, or the real McCoy in college, many of them drop out of mathematics or the sciences entirely; this phenomenon has not gone unnoticed. The Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) in late 2012 released a joint statement on the teaching of calculus.

“Although calculus can play an important role in secondary school, the ultimate goal of the K–12 mathematics curriculum should not be to get students into and through a course in calculus by twelfth grade but to have established the mathematical foundation that will enable students to pursue whatever course of study interests them when they get to college.”

– See more at: http://www.maa.org/news/a-joint-position-statement-of-the-mathematical-association-of-america-and-the-national-council-of#sthash.i7l9KTFP.dpuf

I am all too aware of this situation having experienced both sides, in high school and in college. With this insight, I do everything in my power to prepare students for the course over the summer in a boot camp, and support them throughout the course with many supplemental resources.

Unfortunately, this level of mathematics is challenging for many students, especially those who may have a fixed mindset. Just today, I talked about the importance of keeping an open mind in the course, and working hard at learning, which will improve their chance at understanding the material, succeeding in the course, and ultimately feeling a deep sense of accomplishment. This discussion was in response to concerns over their scores on the first test of the semester, which ranged from a 30% to a 90% with a mean of 65%.

Early on, I also introduce them to the organization, Challenge Success (http://www.challengesuccess.org/), which states: ” we believe that our society has become too focused on grades, test scores and performance, leaving little time and energy for our kids to become resilient, successful, meaningful contributors for the 21st century.” While doing so, I explain that as an AP teacher, and father of an AP student, I understand the pressures they are up against this day and age. I frequently discuss why they should not be too concerned with their grade, or in the case where they feel they must due to our crazy, over competitive system, that they should always seek out someone with whom to speak about their concerns, fears, etc.

Apologies for such a lengthy response. The specifics of the educational dilemma students face, like most things in life, are complex, intertwined, and varied. I wish I could solve it using an Occam’s Razor approach; however, a broadly applicable solution appears to defy even the sharpest of razors.

Thank you for this detailed response and for the Challenge Success link! I would love to know if students attitudes are impacted by their exposure to Dweck. Regarding the other “Sarah’s” reply, it would be interesting to conduct exit interviews when students leave the course. They should exit on a positive note -and I do believe it is OK to provide info that might change their minds — but not so much pressure that they are overwhelmed. For the student who might want to continue in the course as a not-for-credit experience — why not — exposure to the course and observing students who stick-it-out finally get it could be valuable. Thanks again.

Hi Sarah (Chauncey). I survey my students frequently as to their experience throughout the course, as well as at the end. With my MBA and experience as a product manager, I developed expertise crafting effective surveys, which require careful word choice and question construction. While anyone can create a survey these days with SurveyMonkey, Google forms, etc., very few understand the art of questionnaire creation.

In terms of summary statistics from my surveys, in my first year, which was quite turbulent for a variety of reasons, see http://mathequality.wordpress.com/2011/12/30/trial-by-fire-a-mismatch-in-expectations-for-ap-calculus/, students rated their experience in the course on a scale of 1 to 5 with a mean score of 3.76 and a S.D. of 0.68 for N = 37 representing 73% of students; of those students, 93% would recommend taking my AP Calculus AB course. For last year, students’ rating of their experience in the course was a mean of 3.62 with a S.D. of 0.73 for N = 29 representing 78% of students; of those students, 93% would recommend taking my AP Calculus AB course.

I considered suggesting that Espy “audit” the course after dropping it, however, that time had passed by the time I became aware of her decision to drop.

I do not have enough data to comment on whether Dweck’s work makes any (significant) impact on my students’ attitudes towards themselves, their capabilities, and how they handle challenges. I have anecdotal evidence that it does, however, as I mentioned above the vast majority rated themselves as having a “growth mindset” when It is abundantly clear that many are of the “fixed mindset” persuasion, which is a likely reason why those students dropped the course. So the data is quite noisy.

Thanks, John. I hope all is well with your transition into teaching!

Dear Dave, I applaud your passion and enthusiasm for teaching. However, there are a few moments in your description of this event that concern me. The first concern is the lengthy email that you sent to a teenager girl expressing your desire for her to stay in your class. In this email you condescendingly assume that she dropped your class because she doesn’t believe in her intelligence or ability to pass your amazingly challenging class. From what I understand, you never know exactly WHY Espy dropped your class. Honestly, I am horrified at how you patronize this young student without ever attempting to hear her perspective.

You mention Stand and Deliver–unless you showed this movie in class, most teenagers in 2013 have not seen this movie (or read the book) and have no idea why you would mention it in this context. If she did understand the reference, she might view the reference to a movie about Latinos as a disingenuous attempt to relate to her ethnicity. This perspective might not be far off considering your desperate second attempt to relate to the student by bringing up your wife’s ethnicity. Also, your mention of the student’s smile is creepy, and makes me wonder if you would compliment a male student’s smile in such a way.

I am so proud of Espy’s “terse” reply. I might qualify it as assertive. She doesn’t owe you an explanation, especially after that email.

These lengthy emails reveal your own insecurities about your (questionable) teaching methods and your reputation. A few suggestions: if you’re worried that kids are dropping out of your class because of your self-important image (one which you desperately try to refute in the email to Espy), change it. Always ask the student their reason for dropping your class before assuming it’s because they lack self-confidence (it might very well be the opposite). Stop commenting on your female students’ smiles. Wait 24 hours before sending emails to administration and students. Always allow students to help each other in class.

As teachers, we learn from trial and error–it’s the only way to learn in this profession. The key is staying open-minded enough to know when that teachable moment could be happening to us.

Hi Sarah. Have we met? Your prose and other aspects of your writing remind me of someone whom I read online frequently and know fairly well; however, it could just be a coincidence.

Rather than address your concerns point-by-point, which I would gladly do in person over a coffee, or via email, let me just say that everyone sees situations colored by their life experiences (good and bad), internal thought processes and tendencies (e.g. a glass half-full versus half-empty way of thinking), self-beliefs, and value systems. I try to see the positive in everything initially, so I do not unduly burden myself with stress or inadvertently read more into a situation than is there. While I did see positive prose in your comments, and thank your for them, many of your word choices left the impression of a negative, and borderline hostile, characterization of my efforts to reach out to a former student. In fact, your writing embodies the saying that “no good deed ever goes unpunished.”

I wish you did not view my intent and efforts that way, but your perspective is yours, and I accept it. If you have a chance to let whatever chord I struck with you dampen over time, you might go back and re-read the post. In doing so, consider giving the benefit of the doubt, so you can see that my efforts were genuinely well intentioned, even if not the most effective.

Two final comments: 1) my original draft of this was quite lengthy, so it was edited considerably, which leaves out some critical details which might have allayed your concerns, and 2) I did not identify every motive, act, and result in the piece, for fear of sounding more like an anthropologist documenting their every observation. If I had, I am confident the vast majority of readers would never construe my efforts as anything approaching the nefarious nature you see in them. At the same time, they may have fallen asleep as it would have spanned dozens of pages of text.

Dave

Hi Dave, thanks for your reply. I do think your efforts are well-intentioned. I, in no way, think they are nefarious. You clearly care very much about teaching kids how to think rigorously about math.

Unless you can tell me that you actually heard from Espy, or at least someone, that she dropped your class because she lacked self-confidence and faith in her skills, I stand by all of my comments. Asking her why she dropped your class before sending her a lengthy email rife with faulty assumptions about her self-esteem might have been more effective at re-enrolling her in your class.

I don’t think your compliment of her smile or your attempt to connect with her with a movie reference or a bringing up a commonality were malicious. I just hope that you recognize the power differential between a male teacher and a female student–not just in this situation but in all situations.

I’m not totally certain what the readers were supposed to gain from your post? What did you learn from these events? What we were supposed to learn?

What I learned is that you’re proud of yourself for working so hard to convince Espy that she is smart enough for your class (even though you’re not sure that’s why she dropped). And you’re disappointed in her for not recognizing your efforts and being grateful enough for them that she re-enrolled in your class so you could carryon with your attempts to teach her math in a way that she has never been taught math before. You also seem disappointed in the administration for not recognizing the sacrifices you made and complying with your demands (you did, after all, used to make more money than all of them).

PS. You know who would advocate allowing students to help one another in class without being “chastised?” John Dewey.