Inadvertently Shortchanging Students: Angelica’s Story

Holding students to high expectations is not just for teachers.

A Disrupted Morning Ritual

As I counted off students in my fourth period AP Calculus AB class early this morning, 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, this is especially problematic.  During this early stage of the course, 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, neither of which is the intent of any calculus teacher.  Yet, such is the beast of an advanced mathematics course like calculus.

By the end of the second week of class, students who are highly unlikely to be able to handle the demands of the course have either dropped for AP Statistics, or decided not to take any mathematics course their senior year; given the advanced nature of the course, most students who drop are seniors.  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 just finished that necessary phase of the course.  They were now preparing to hunker down for the demanding nine months ahead of them.  One quiz on limits was under our belts, with our first unit test covering limits and continuity planned for the day after Labor Day when we returned from the short break.

So, it was with great apprehension earlier this morning that I opened my online attendance roster and immediately noticed that the number of students in my fourth period AP Calculus AB class had declined by one overnight.  I needed to sit down, as I felt a wave of emotions heading my way.  Scrolling 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.  Fortunately, students needed to learn about the average rate of change, as well as the instantaneous rate of change.  My mind readily embraced the opportunity to help students understand these all too important foundational concepts of differential calculus.  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, a couple of students lingered during the morning’s ten minute break period, as they needed help with a couple of homework exercises.  Once they wandered off, satisfied with the help I provided, my mind revisited the emotions I felt earlier in the morning when I learned that a student, Angelica, dropped my course.  Anger turned to sadness as I reviewed her transcript and GPA.  Angelica 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 (“CELDT”) 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 Angelica’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.

Opening the essays Angelica wrote for summer work, as I required my incoming students to write about themselves and mathematics, I noted that she 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.  She also noted how important it would be to brush up on her prerequisite skills, so she could succeed in the course.

Yet, those words no longer carried significance for Angelica, at least for my AP Calculus AB 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 felt compelled to speak my truth about what I strongly believed to be a tragic situation.  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.  Select content regarding mathematics curriculum and pedagogy has been embellished in the editing process for this blog posting.  Nonetheless, the gist of the message remains the same, as does the majority of the content.

I am very disappointed that Angelica 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, Angelica is not one of them, at least from what I know currently.

Angelica 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 AB 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.  Just as in Ramon’s case, I invest a significant effort in working to convince a student I know can pass the course to stick with the challenge, if I know of their intention to drop beforehand.

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, their action has the exact opposite effect than they intended.  

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.  

Additionally, mathematics challenges a majority of our adult population, as well as K-16 students, primarily due to the way it has been defined as a curriculum, and its well intentioned, but very ineffective decontextualized, oversimplified, and too teacher-centric instructional methods; this is not solely to promote a pure discovery approach either.  What is needed, as with most things in life, is a situation dependent, balanced approach where direct instruction and discovery learning are intertwined in a complementary fashion.   Use of these two pedagogies need not be considered mutually exclusive.

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 a decontextualized, oversimplified, and directly taught environment.  However, when they face something slightly more complex, specifically in a form they have not yet encountered, 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 tenacity has been calibrated to no more than a “repeat what the teacher shows you” level of challenge; it 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, or online learning environments.  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.  While it is with the best of intentions that we enact our various policies, procedures, and methods, we are frankly, as a nation, failing ourselves, and our future.

I remain deeply saddened by Angelica dropping my AP Calculus AB 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.  Angelica 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 Angelica’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 Angelica in those circumstances.  Just today, with another student, Sylvia, who I hope is receiving counseling support for what seems to be a challenging situation in her life, I took the opportunity to inform Sylvia that she simply needs to let me know how I might help her as she deals with her challenge.  This is how I believe we best help our students develop into their full potential.



PS I know that in their request to drop AP Calculus, many students complained that the course is 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.  As I mentioned earlier this year, I am a strong advocate for helping students develop a “growth mindset.”  Yet, if 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 Angelica

A few minutes after sending my email message to my administrative team, I composed and sent a separate email message to Angelica in hopes that she might reconsider her decision.  I did not have the opportunity to seek her out immediately, so I chose the next most immediate method: email.  Since I extensively use electronic and online means with my students, I had her email address at the ready.

My words to Angelica follow.

Hi Angelica.

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

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.

Angelica, 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. Math Teacher

 A Personal Delivery

Even though I sent emails off to both the administrative staff, and Angelica, I felt compelled to do more to ensure Angelica received my request, and that she carefully considered the possibility of rejoining the class.  However, as the course would march on with new content, concepts, assignments, and assessments, time was of the essence.

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


Angelica’s sixth period teacher not only delivered my message to Angelica, 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, Angelica had not one, but two more advocates, besides myself, 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 Angelica’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 Angelica.  I hope that she rejoins the class.  Only time will tell.

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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11 Responses to Inadvertently Shortchanging Students: Angelica’s Story

  1. Dave says:

    As usual, you never fail to amaze me. Never in 13 years of teaching have I heard of someone who would go to these extents for their students. I have some of your characteristics but never went those many extra miles. Unfortunately your intelligence and persipacity surpaces those of your superiors. Fortunately you have some fellow travellers among your peers. Good luck, you’ll need it.


    • Thanks, Dave. I needed to look up perspicacity. That is probably on some Kaplan GRE or GMAT vocabulary card set I used a while back!

      I’ve read of exemplary teachers going well beyond my meager actions. However, I do hope my efforts were not in vain. And I do hope Angelica returns.

      Hope all is well.


  2. PLu says:

    After a 41-year math teaching career, one of my saddest observations is that administrators don’t always make the best decisions—–in fact, are human! Hopefully this situation will be a growth point for them too, if they choose to read and take to heart your letter. Keep fighting the good fight!


    • Thanks, Peggy. One of the things I’ve learned in my almost 50 years is that we are all human, make mistakes, typically act in the best intentions, and absolutely need to understand other people’s point of view.

      As I wrote my letter to them, and this post, I wanted to make sure I respected them as I knew they did what they felt best at the moment. I do hope they understood where I was coming from as well.

      I really like my administrative team, all of them. I’ve spoken with each of them at times, and some at great lengths. I believe they trust me and I trust them. I just believe we need to work a little closer together on certain situations, like the one in this post.



  3. russtowne says:

    I’m glad to know such a dedicated teacher who works hard to truly serve his students! Way to go, Dave!


  4. mrdardy says:

    I think what impressed me most here is the depth and care you showed in constructing that letter to your administrators. I have had the exact same situation you’re describing here (sadly, also related at times to wanting to avoid me because of rumors about how hard life can be in my classroom) and I have never been able to muster the eloquence you showed here. Bravo and here’s to a successful return for Angelica.


  5. Kiera says:

    Dave, tears welled up in my eyes too. You have given an important gift to Angelica. Whether or not she rejoins your class, she now will know for the rest of her life that a very smart, very talented and very demanding calculus teacher believes in her and believes she has what it takes to achieve things that most of her fellow students could not. I will start my work week tomorrow with increased purpose. Thank you.


    • Thanks for being able to see my intention, Kiera. An edited version of this was reposted on a separate blog, where a reader of it tore into me in the comments section. I am always surprised when the pain someone experienced in life colors their interpretation of events, real or perceived. I will email you the link to that post and comment thread separately. Good luck with the start of your week! I hope I make it up to Chitown someday so we can reunite our families for dinner at Maggiano’s or even Portillo’s! 🙂


  6. Jack Dieckmann says:

    I was very moved by this account. For me, it highlights a critical ability of teachers to keep high standards, but to also assure students that help is always available. Dave, you could see potential in this student, and hopefully, it will help her see it in herself. The conundrum for me is that students who have talent often do not make good use of it, and that is part of their agency as people. Everyone needs the opportunity to learn from their choices. I think giving her more information and encourage was the moral thing to do. We need to relieve teachers from many tedious duties so that you can use your energy to fight for kids like Angelica!


    • I could not agree more, Jack. There is a definite opportunity cost to the myriad tasks facing teachers on any given class day. I hope we wake up and make true change in education soon. It’s archaic form and function precludes progress and rewards conformance rather than innovative improvement. Sad. Without radical change soon, I see the slow but steady erosion in the potential intellectual capital of our nation leading towards a regression of the mean, otherwise known as the “stupidification” of America.


  7. Pingback: Notes of Thanks | Reflections of a Second-career Math Teacher

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