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MASTER TEACHER PROMOTION
2020/2021 Academic Year
INTERVIEW QUESTION RESPONSES
Describe your professional development plan, particularly its link to your last evaluation. This would include some combination of books you have read, resources (magazines, electronic mailings, etc.) you subscribe to, conferences you have attended, teachers whom you have visited, educational organizations to which you belong, etc...
My professional development plan has evolved in three directions. I have employed PD to 1) grow my range of pedagogical practices, 2) contribute to the goals of the math department and 3) better understand the lives and experiences of my students to become a stronger relational teacher.
In terms of growing my range of pedagogical practices, I had an awesome experience at the University of Pennsylvania GSE Project Based Learning Certificate Program. I attended with several Haverford colleagues and we spent two consecutive summers and the academic year in between learning the principles of PBL and finding ways to incorporate them into our classrooms. I feel fortunate that Penn PBL has invited me back for the Summer 2020 Institute to lead a workshop on supporting teachers in assessing PBL.
In terms of contributing to the goals of my department, in the summer 2020 I attended a professional development training for the curriculum we use in Algebra I, Algebra II and Calculus called College Preparatory Mathematics or CPM. CPM employs a powerful pedagogical framework based on problem-based learning, collaboration, and mixed/spaced practice. I introduced CPM to the department 2 years ago, having taught it other schools, as a possible good fit for our Algebra I, a course which was at a transitional point in our course offerings. Since then, members of our department and, even more importantly, students at our school have really come to see the success in its approach, and so I joined a small cohort of our math teachers in attending the Phase I Implementation training so we can learn more about how to employ it to benefit our students.
Finally, early in my time at Haverford I recognized that there was the leadership and vision to support me in my longstanding goal to better understand the lives and experiences of my students of color. I began my career teaching in schools that more directly served communities of color, but since teaching internationally, I found myself increasingly out of touch with this population and alarmingly, I began to feel as though many of the well-intentioned approaches I took earlier in my career now appeared very problematic in light of my more recent reflections. During a Diversity and Inclusion committee meeting, I became interested in a Race Institute reading of the text White Fragility that was held at Haverford, which subsequently drew me to a Race Institute Workshop in Summer 2019, which then prompted me join a SEED Cohort during the 2019/2020 academic year, and now I am so energized by this work that I am facilitating faculty readings in an effort to improve my own racial literacy and that of our communities. These last PD experiences have been some of the most profound and influential in my career.
I feel incredibly lucky that Haverford has supported me in growing in these directions and I hope to give back to the community as much as I have received.
STRENGTHS
What particular professional strengths qualify you as a Master- someone who could be a model and mentor to new teachers? What sets you apart from the other Experienced Teachers? Articulate what effective teaching is. Speak to the difference between the science and art of teaching in your classroom.
I believe that the particular professional strength that qualifies me as someone who could model and mentor new teachers is my commitment to supporting teachers in their efforts to meet their goals for improving their practice. In every opportunity I have had to support my colleagues, my first goal is to build a relationship with them in which it is clear that I have removed any perception of my agenda from their decision-making process. I make it clear that I see my role as helping them to clarify their goals, identify challenges and parameters, constructively push back when their actions do not meet their stated goals and to make available all the information and resources possible to ensure growth and success. Fundamental to this process is careful listening. I need to do more than listen; I need to hear and see the situation from their perspective to fully understand their desired outcomes. I need to be clear about the context in which they are trying to achieve their goals, and this often requires that I do homework and ask questions outside of my meeting with the teacher. Finally, I need to consistently remind both myself and my colleague that my colleague's success is my sole objective. I have been enormously influenced by the work of Elena Aguilar and specifically her book The Art of Coaching. Three experiences come to mind when I reflect on this question:
I am lucky to have served as a Mentor Teacher a few times in my four years at Haverford. Each experience was distinct from the others in terms of the areas in which we focused our discussions, so that I grew tremendously as a result of all three professional relationships. The first teacher was someone who knew our Haverford community extremely well and who brought a special set of skills and perspectives to his role, but who was still new to the teaching profession and wanted support in refining his pedagogical craft. We discussed frequently the topics of assessment, student-centered learning and pedagogy. The second teacher was a very experienced educator who was an expert in her field, but was new to teaching high school and so we frequently discussed how to translate her brilliant ideas into modalities that were accessible to her students. The third teacher was similar to the first in that the teacher was new to the teaching profession, but hadn't yet formed core philosophical elements of his teaching identity. We speak most frequenly about those aspects of the profession. It was an honor to work with all of them. Being a part of the Mentorship Team may be the most rewarding project I have been involved in at Haverford.
My experience running IC Day was another instance in which I had the opportunity to work with my colleagues to develop and implement their ideas for this awesome Haverford tradition. Briefly, in addition to supporting teachers in executing the logistics of the day, my goal was to support teachers in taking the work they had done in previous years and focusing the learning around essential or guiding questions that renewed the practice of intellectual inquiry. It was fascinating for me to see the myriad of perspectives and talents my colleagues bring to the Haverford learning environment everyday and I hope I played a role in supporting them to implement their ideas for the day more effectively.
Finally, it has been the greatest challenge and area of personal growth to have lead two Anti-Racist reading groups over the past year. First with the text, White Fragility and then with the summer reading of How to be an Antiracist, my goal throughout has been to use the profound messages of the text to support teachers in growing their anti-racist teaching practices at Haverford. I have focused on generating activities and discussion questions that constructively provoke reflection and conversation, but that ultimately translate into action. I have been mentored and aided by numerous colleagues at the Haverford School, and I have been happy to contribute in this small way to the larger school-wide initiatives currently underway. I will speak to this in more detail below.
CURRICULAR INITIATIVES
Describe initiatives you have taken to improve the curriculum. Have you gathered teachers for vertical or horizontal curricular review or alignment? Beyond the walls of your classroom, how have you leveraged your expertise for the betterment of the curriculum? Give a few examples that demonstrate that you are a team player in curricular development.
I would like to return to two items I named in response to the "Professional Development" prompt above and elaborate on how these two professional development experiences gave me the opportunity to further support curricular initiatives undertaken by my department. In many ways, these PD experiences, and the tools they provided, really contributed to serving the same goal which is increasing the scope and efficacy of student-centered, inquiry-based pedagogies in our math department classrooms. Here, I am referencing specifically my introduction of the math curriculum College Preparatory Mathematics (CPM) into the Haverford math department and my work with the U.Penn Project Based Learning Certificate Program.
I mentioned above that I introduced CPM to the department in my first year at Haverford during the 2017/2018 academic year as an alternative academic program to the one in place in our to the Algebra I classrooms. Algebra I is a tricky course, as I have spoken about elsewhere on this website, in that it services students with a range of mathematical experiences, but who have ultimately decided that an extra year of solidifying the foundational Algebra I concepts would be beneficial. This includes students who had already taken Algebra I and struggled, who had taken a non-traditional Algebra I class such as an integrated 8th grade course, or who had no experience with Algebra I at all. As I understood it, the curriculum prior had been heavily focused on rote skill building and specific review of topics as needed, rather than a comprehensive course that focused on students developing conceptual understanding and seeing the mathematical connections between the topics. The online tool Aleks was used heavily to track student progress. Where this might seem student-centered, my contention was that it didn't do enough to address the roots of student misunderstanding and in many cases the resulting disengagement from and lack of enjoyment of the profound beauty of the study of mathematics. The student-centered learning I was interested in focused on inquiry, problem-solving, collaboration, building community and confidence and developing critical and creative thinking skills. My argument is that if these qualities are the focus of the learning, the skill building will follow. CPM gave me the ideal platform upon which to build out my vision of the Algebra I class, and I am thrilled that many of my colleagues in the department agreed. In subsequent years multiple teachers with many years of experience teaching Algebra I co-taught the CPM Algebra I course with me and immediately saw the improvement upon the old curriculum. Both department chairs I have served under have also recognized the power of the curriculum, and have initiated rolling the CPM curriculum up to the Algebra 2 and Standard Calculus courses. In the Spring of 2020, I visited our middle school and guest taught a class to Haverford 6th graders and the middle school teachers who observed the lesson noticed the engagement and enjoyment experienced by their students. I have had the pleasure of supporting my colleagues in better understanding the philosophies and techniques of the CPM program across divisions, and I look forward to continuing to be a resource and an advocate of the program moving forward.
Secondly, as I mentioned in response to the "Professional Development" prompt above, the U.Penn Project Based Learning Certificate Program provided me a broader set of tools and vocabulary to think more deeply about student-centered learning, which is, at this phase, a general curricular initiative of the department. There is widespread agreement amongst the department as to the value of moving math learning at Haverford in this direction, and the decision making power to do it, the question simply remains the pragmatic one of how and according to which models. Fortunately, I found, and my colleagues who attended the U.Penn PBL program concur, that the tools and vocabulary the program used as their orienting paradigm are general enough to be constructively applicable in the contexts of a "project based learning", "problem based learning" or some other hybrid modeled classroom. I am happy to be able to bring my learning from that PD experience in forwarding my department's curricular initiatives.
LEARNERS AS INDIVIDUALS
What steps do you take to know your learners as individuals? How do you design and deliver your curriculum to target the individual learners in your class?
The global strategy I use in my classroom to know my learners as individuals is that I commit to a student-centered, inquiry-based approach to plan all of my lessons. What this means in a working sense is that I approach my teaching from the constructivist philosophy, which espouses that students learn more effectively when they build their own understanding of the material by doing tasks and exercises that allow them to discover the concepts and skills, rather than passively listen to me teach them. This allows me to know my learners as individuals because rather than having my focus be on myself delivering content, it is on them and how they are processing the content as they work collaboratively. When I plan a lesson, I anticipate that I will spend at least 50% of the lesson time rotating amongst groups, listening to them build upon and critique each other's ideas and engage in scaffolded Socratic questioning techniques. In this format, I have the opportunity to observe the students’ learning personalities in action and register which students process verbally, which benefit from visual tools, which learn best by listening and synthesizing ideas, which learn by attempting the task individually before collaborating, and so on. In my lesson planning, I design the task so that it has a consistent structure so that students can anticipate how they will be expected to engage with each other, with me as their teacher, and with the learning. I embed exercises that prompt students to meta-cognitively reflect upon and share their preferred learning styles, and I benefit enormously from hearing students describe their perspective on their own learning. Furthermore, I plan to connect with parents through my newsletters and invite them to share their understanding of their son’s learning styles and experiences with me. I will address these newsletters more below. Finally, academically, I believe that by transitioning my assessment protocol to reflect a Criterion-Based Grading approach has allowed me to explicitly acknowledge and provide feedback on my students’ specific learning styles and how they align to my expectations of them for the course. In a recent survey, on the question of Criterion-Based Grading, one student responded, “I like criterion-based grading because it judges your other attributes than if you actually got the right answer or not. I think this takes a lot of stress off of students to get the right answer. Rather, students will focus on communicating ideas with each other. Overall, I think it is really great for the students.” Those “other attributes” I take to mean the way students creatively investigate, the way they effectively communicate, and the way they constructively collaborate around the learning that happens in the class.
Outside of the classroom, I understand my role as an educator to be one of a support source for all aspects of my students lives. To this end, I commit myself to attending at least one match for each sport of each season with special equitable attention to those hard to reach hockey and wrestling tournaments in the winter or crew regattas in the spring, and attending at least one performing arts event. I also try to plan in my calendar to visit each club event whether that be a Diversity Alliance film screening, a Robotics or Speech and Debate tournament or Model UN Conference. It’s not always easy with young children, but often times I have found that at least for my oldest, it is a lot of fun sharing these events with my family, and sharing my family with the broader community. Nothing beats the smile that erupts on the students’ faces when you ask them about a particular moment in an event that you observed. I hope it communicates to the students that I care about their lives and interests outside of my classroom, because I wouldn’t be in this job if I didn’t.
CURRICULAR EXPERTISE
What area of curricular development do you believe you are uniquely qualified to lead and how have you intentionally developed expertise in that area? If I were send a teacher to observe or speak to you, what particular area would they have been struggling with? If you were to present at an area conference, what would be your topic?
On the topic of curricular expertise, I feel most qualified to lead in the domain of Assessment. Early in my teaching career, something didn’t feel right to me about how we assessed and provided feedback on student learning. The problems I intuited at the time were recently nicely expressed by Jack Schneider of U. Mass Lowell on the radio program 1A, namely that in grading, education conflates too many objectives, often contradicting, into one tool. I spent time grading in traditional systems, “progressive” charter systems, International Baccalaureate systems, and French systems, and all experienced the same issues, albeit in different ways with different strengths and challenges. The tension in my relationship with assessment came to a head in an interview I had with a principal and director of school for a position teaching overseas in Morocco. In the interview I was asked, “When a student receives an 83% on an assignment, what does this say to the student?” My jaw dropped slightly and after a few seconds of processing all I could say was, “Nothing.”
I took the job at the school in Morocco and helped to launch a Criterion-Based Grading program, which used traditional qualitative metrics, but rather than arriving at those metrics based on percentages and points, they were exclusively arrived at through the use of rubrics. Additionally, I helped in designing and implementing the school wide criterion that would be found in every teacher’s grade book, those of “Knowledge and Understanding”, “Investigation”, “Communication”, and “Learner Skills”. Since arriving at Haverford, I have integrated this system of assessment into my classrooms and I have been invited to lead workshops supporting teachers with assessment at conferences held at the Center for STEM Education at San Francisco State University and in the Project-Based Learning Certificate Program at the University of Pennsylvania. I believe the system that I am continually evolving in my classrooms would be an excellent fit for the style of learning we at Haverford will need to employ in our hybrid learning environment. Additionally, and perhaps most importantly for me, I believe that this system of assessment is the exact type of anti-racist practice and policy that I continually aspire to. It is anti-racist because it eschews narrow definitions of mastery of learning that historically have privileged students who benefit from the resources to excel according to these definitions, and explicitly recognizes and rewards students for the creativity and diversity of contributions that all my students can bring to the classroom. For more on Criterion-Based grading, you can read about it and my motivations for using it in my classroom on this page.
EFFECTIVE PRACTICES
How do you generate ideas for creating a classroom environment conducive to learning?
List five of your most effective practices.
5 practices that I believe are effective to my creating a classroom environment conducive to learning are:
Complex Task design
Open Questioning, Wait time
Random grouping
Assign Confidence
Include students in making decisions about assignments
Complex task design is intended to challenge all students with tasks that require a range of skills, perspectives and thinking modalities in order to solve the tasks most thoroughly and effectively. These tasks are designed to be sufficiently complex to require collaboration, but are inherently differentiated because they are designed to be accessible from a variety of perspectives and learning abilities. They require proficiency with the content skills, but skill development isn’t the purpose of the task, rather the goal is to elicit inquiry and critical, creative and collaborative thinking. I frequently reference Vygotsky’s Zone of Proximal Development to the students and explicitly tell them that I design and adapt problems that I research so that the task is just outside the comfort zone of any individual student, but that collaboratively the students can grow significantly by working together to solve them.
I scaffold the learning that happens around complex tasks by asking open questions (rather than closed questions for which the student answers can be responded to with “correct” or “incorrect”). Open questioning techniques elicit divergent thinking, prompt the development and sharing of ideas, and welcome new, diverse perspectives. Open questioning allows students to build on each other’s contributions for the purpose of driving the conversation forward, rather than closing it down with the misconception that we’ve arrived at “the answer”. This sometimes leads the discussion down unexpected paths, that I have the choice of following or redirecting, but I have found that this allows truly intellectually authentic connections to emerge, and the students have reported enjoying the philosophical digressions. Essential to open questioning techniques is the employment of wait time, which is at minimum 10 seconds for students to process the question, formulate responses and wonder. I often literally count in my head or quietly with my fingers at my side to hold myself accountable to providing students this time.
I insist that the vast majority of grouping arrangements is done randomly. I tell students from day one that random grouping accomplishes two things: 1) It ensures the creative cross pollination of ideas and the blending of learning personalities that would not be possible if students choose their own groups, or if the groups are designed by me. Students often find others in the class who are not in their circle of friends and so who they normally don’t interact with, but who are constructive learning partners and with whom they go on to form productive study groups outside of class. 2) I have lived through the moment when a student enters the classroom and is forced to decide where and with whom he is going to sit. For many students, this is a terribly anxiety provoking moment and introduces a host of social status concerns that I want to monitor, but that I do not want affecting the dynamics of the broader learning community. I do not want students to feel excluded or embarrassed at not being selected. I am happy to absorb the frequent annoyed glares when I deny students working with their friends because I know that my rule prevents the social tension that choice seating allows. I insist the groups are random by drawing playing cards, so students aren’t left wondering whether, why or how I chose the groups. Finally, the students learn they need to be able to work productively with any personality they might be grouped with. I believe this is an important life skill, and it is one for which I intentionally build scaffolding activities for productive development.
The Complex Task design, Open Questioning and Random Grouping all establish the foundation for me to do what I have heard defined as Assigning Confidence. As students collaborate, I have the opportunity to observe the dynamics of the learning. I ask myself questions such as 1) who is talking, and to whom 2) how are students seated, who are they facing, from who are they turned away 3) how are contributions recognized and built upon, how are they ignored, how are they critiqued? The answers to these questions help me to understand the dynamics of social and academic statuses amongst the students. Assigning confidence is the intentional act of acknowledging and elevating the constructive contributions of low status students. They serve to both leverage my authority as the teacher to impart praise to the student, and to publicly recognize the contribution to communicate that all students have valuable contributions to make. The act is necessarily public either within partnerships, small groups or the whole class, but the public nature of the act sets a tone for the entire class to follow.
Finally, I try as much as possible to include the students in as many acts of decision making as possible. Whether it be stretching a learning task into another day, choosing a due date for an assignment, or refining the wording on a rubric to better capture the learning expectations, by making these decisions out loud and eliciting the thoughts of the students, everyone gets to feel that they have a key role in deciding how the class will be run. I communicate transparently my thoughts on the matter, set any parameters necessary, but ultimately invite critical questions to my thinking and student preference. The goal is ultimately to power share in order to reinforce the message that we are all equally involved in this learning community.
Indeed, all of these strategies are intentionally designed to build community through establishing relationships of trust and support. I believe that establishing such a community is perhaps the most important step we can take to ensure we provide the best conditions for learning.
CHANGES TO CLASS ENVIRONMENT
What are 2 changes you have made in your classroom environment? What are the reasons for the changes? What has been the outcome?
The two recent changes I have made to the classroom environment that I would like to discuss here are 1) Group Work Roles, and 2) Criterion Based Grading - Learner Skills.
I have dabbled with implementing formal group work roles in my teaching for the past 8 years. I have done so with more success and confidence when I have taught middle school. In my experience the MS students seem to have been more receptive to being assigned tangible roles than my high school students, maybe because they are young enough to not feel patronized by the micro-management of their learning behaviors or just see themselves as needing to learn the important learning skills assigned by group work roles. But whatever the case, over the past year and heading into next, assigning group work roles will become a significant feature in my classroom. Observing how my students interacted virtually last Spring, and noticing the differences between when group work roles were part of the learning task versus when they were not, I realized that especially now, students require and want more structure for their online collaboration. The four roles I use in my groups are those of:
Facilitator - primarily responsible for facilitating group work norms like making sure everyone has a chance to share their ideas, prompting group members to justify the reasoning of their contributions and summing up the collective answer,
Task Manager - primarily responsible for keeping the group on task, making sure everyone understands the problem and keeping track of the time,
Recorder/Reporter - primarily responsible for recording the group’s thinking and sharing it out to the class,
Resource Manager - responsible for any tools or resources the group needs such as support from the teacher, rulers, calculators, markers, poster paper and in the virtual environment, screen sharing.
I will be more prepared to address how the students responded to this feature of the classroom environment in a few months, but from what I saw last year, groups were able to begin working through their task more efficiently knowing who was responsible for what, and I believe students were able to achieve greater levels of engagement knowing that they would have an important and well-defined role to play in helping the group optimize their learning. The challenge will be implementing group work roles in a way that students aren’t made to feel patronized or silly and so that they take the roles they are assigned seriously.
I have already discussed at several points the second classroom environment change I have recently made, that being Criterion-Based Grading, but now I want to dig deeper into one of the criterion that was particularly important for both my “Honors” and “Standard” level students, and that is the criterion of Learner Skills. For the Honors students, one of the biggest misconceptions that I believe persists within the Haverford community is that the honors students “already know how to learn”. This may be true to the extent that they know how to execute simple tasks like getting their homework done and understand the terms of getting a good grade more broadly. But from my time with the honors Pre-Calculus students, I have observed the extent to which they struggle with more complex meta-cognitive and executive functioning skills such as iteratively reflecting deeply on their problem solving process to catch and learn from misconceptions and mistakes, collaborating constructively, taking productive notes that they can learn from and effectively managing their time, to name a few. By creating a grading category explicitly designed to help them with these skills, I am now able to address them directly on the rubrics for their learning tasks, provide feedback where needed and assign confidence by using their growth as exemplars. I was met with some resistance at first, but in surveys throughout the year, a number of students commented on how much clearer the learning objectives became when we disaggregated and focused on these skills separate from the test or project grade. For the Standard students, learner skills such as basic note taking, organizing a binder, studying, submitting assignments and keeping a calendar have long been a challenge. I was thrilled to partner with Mr. Steve Cloran from the ELC who would visit my Algebra I classroom on several occasions at the start of the year to impart his expertise to the students and so we could break up into smaller groups and workshop particular skills. The younger Algebra I students are equally frustrated at first at the insistence of focus on these skills, but as the year progresses and as they see the quality of organization on their binders improve, they become aware that the explicit instruction on these skills was well worth the time.
MEASURING EFFECTIVENESS
How are you measuring your effectiveness as a teacher? This could include
but is not necessarily limited to student feedback forms, common exams or exam questions, standards based curriculum design or assessment, anything external that guides you in the design of your curriculum and that suggests you are not the sole judge and jury of your effectiveness.
The two primary ways I measure my effectiveness as an educator are that 1) I frequently employ the use of student surveys in seeking their constructive feedback, 2) I welcome regular visits from faculty to observe my classes, and mine theirs, and we debrief our observations at a later date.
I have cited now several instances in which I have gained key insights after soliciting feedback from my students. Student feedback is a particularly compelling measurement of effectiveness because it often reveals my blind spots as the teacher. More than giving me information about how well I explained a particular topic, student feedback measures how well I understand their experiences and expectations for the class, which I believe is fundamental to creating a successful learning environment. If I can’t understand how students are feeling about my class, then it can’t be said that I am designing an optimal student-centered task. In designing most of my student surveys, I invite students to talk about themselves and their relationship with the course. Their answers are revealing because if I ask them, for example, how they feel about their ability to identify the meaning of a problem and to develop ideas about how to begin it, and they respond less than positively, since I have defined that as a key goal for my students in my classes, that indicates to me an area that I have failed to address in my teaching to the extent that I need to. I then know what I must do to ensure that the students have every opportunity to improve in that regard. Here is a link to one of the surveys I use in preparation for March Comments (if you would like to peruse the survey, use the “Test” selection for Class, and enter “Test” for your name). I use the student feedback to write my comments, but importantly for what I am addressing here, it indicates to me where I need to improve in prioritizing lesson time for the rest of the year.
Additionally, I frequently welcome colleagues to visit my classes and ask them for constructive and critical feedback from their observations. Faculty observations provide insight and perspective that only colleagues with training and experiences in our profession can offer. Our current Department Chair, Justin Gaudreau has made this a priority and greatly facilitated our visiting each other’s classes by making our teaching schedules available to each other. The ongoing CPM curriculum project has provided an ideal opportunity not just for those teachers co-teaching Algebra I with me to observe, but also our regional CPM rep, Algebra II teachers, middle school teachers, and even our 5th grade math specialist. I recently had the pleasure of inviting Mr. Gaudreau, Mr. Mark Fifer and Mr. Jamison Maley to observe a number of my classes as part of my Full Faculty evaluation. And finally, being part of the Haverford Mentorship Program for the past 3 years has given me a number of opportunities to welcome new faculty members to our Haverford community to my classroom, which has produced particularly fruitful discussions because they bring new insights and perspectives from their experiences teaching prior to Haverford. I always get a little nervous when I am expecting a visit from a colleague, but I have found that at Haverford these observations have always been conducted with growth, gratitude and respect for all parties involved and this has made it infinitely easier to actually hear the feedback and ideas for implementing it into practice.
EMERGING TECHNOLOGIES
What are the best and worst things that emerging technologies have done for your instruction? What tech capacities do you think today's learner needs to be proficient at and how are you using your class to develop/deliver them.
I believe the best aspects from emerging educational technologies pertain to the differentiation of presentation of content and the opportunity to move away from a curriculum based on knowing facts and into the more important inquiry and problem solving spaces. The worst aspect from emerging technology is not actually an element of the technology itself, but a misbelief about it. I will take each in turn.
Technology has given me a range of tools for which I can support students in making meaningful connections with often abstract and analytical content. Fundamentally, it has broadened my ability to communicate. For example, the mathematics of finding the intersections of vector lines through 2D planes in 3D space is terribly esoteric and inaccessible to visual learners like myself. It involves complex formulas and numerous procedural steps. But when I can use this Geogebra visualization (feel free to play with the tool by click holding on an area of the space and turning) to articulate the meaning of the task in front of us, most of the students in the class can literally see the nature of the problem. It does not relieve us of the mathematical processes, which is part of the syllabus, but it grants access to students who first need to visualize the problem in front of us. Geogebra was a great tool again for making the connection between vectors and rotary motion as in this visualization of gum being stuck to the bottom of a bicycle tire (press the play button in the first formula field to watch the wheel roll). Or this Desmos visualization made by my colleague Mr. Matt Ator of the famous Double Ferris Wheel problem (again, click play). These visualization technologies also allow us to differentiate the end product of student research, as is the case with these Desmos representations made by students BW and CL (double click to zoom and click and drag to follow along the x-axis) of the famous Pendulum Wave experiment. I would be remiss if I didn’t mention the impressive PreCalc* Website that Haverford students have created over the past two years. Creating and posting their learning to a public website makes the learning process authentic because they know they have a real live audience who can learn from and comment on their work at any point. This range of communication tools extends beyond just visualizations and allows me as the teacher to record and post to any number of communicative mediums further explanations about particular concepts or skills. Now, due to the coronavirus, teachers across the country are recording mini-lectures and posting them to their channels. I started this practice when I arrived at Haverford 3 years ago because Haverford was the first school at which I felt that I actually had the bandwidth in my teaching load to begin a robust online video recording project. I was thrilled to be able to contribute to Mr. Sam Walters’ phenomenal Geometry textbook from which almost every Haverford student learns their Geometry by creating customized videos posted to Youtube on problems in the text that students year after year can watch and learn from. So there are a number of emerging educational technologies that contribute enormously to the differentiation of presentation of content both from teacher to student, but of course from student to teacher as well.
Perhaps more important than differentiating communication of content, is the ability of emerging educational technologies to allow the focus of the classroom learning to be on the vital critical and creative investigation and problem-solving thinking skills we as a society so desperately need to confront 21st century challenges. There are so many platforms that now do the traditional mathematical coursework of computation including the before mentioned Geogebra and Desmos, but also, more powerfully, Wolfram Mathematica and Matlab. The focus on the classroom learning must shift away from the teaching of computation for computation’s sake, and into the realm of problem solving for the sake of solving real problems. Emerging educational technologies have contributed to this in my classroom in the research of the mathematics of the fastest cyclist on earth, the physics of propellers, motion and sound, and to create art. The technology was able to introduce the students to the mathematical problems inherent in these fascinating phenomena, and to assist us in the complex computation, so that we could concentrate on the creative, critical, interpretative and iterative aspects of research.
If these are the benefits of emerging educational technologies, then the downside is the misbelief in the inverse: that since technology can perform complex computations, that we no longer need to include these skills in the curriculum, and that technology is the superior medium through which to teach them. The first argument goes that since we have computational tools to do complex computations, we no longer need to teach the skills. This fundamentally reflects a very narrow understanding of mathematics, and I believe other educational subjects as well. Speaking for my own, this misbelief communicates that mathematics solely operates in service of applied natural and social sciences. It ignores the beautiful philosophy of the subject, the rigorous language and the mind-boggling conclusions it draws. When students are performing the skills on their own and see how the skills are logical manifestations of the concepts, it simply inspires wonder and the confidence to investigate the logical threads independently. This is how much of mathematics has been discovered. The second argument acknowledges the need to teach skills, but overestimates technology’s ability to do so by underwhelmingly reducing the performance of skills to some arbitrary standardized test or credentialing process. Although the founders and creators of Khan Academy and Coursera are on record stating that this was never their primary intent for the platforms, interests who seek to systematize education more efficiently have held these tech platforms as the answer to “bad” or “ineffective” teaching. I acknowledge the brilliance of these platforms as tools and resources, but they can’t replace the relational teaching, creative spontaneity, and the organic wonder that only communicating with a live teacher and classmates can provide. Same too goes, in my mind, for the belief that online assessment tools provide the answer for the problem of quickly assessing lots of students at once. The assessment these tools provide can only capture the first level of Bloom’s Taxonomy, not the elements of teaching and learning that education should really focus on and that true assessment and feedback should really be tasked with addressing. So the worst aspect of emerging technologies is not the technology itself, but the misplaced beliefs that the technologies can make teaching and learning cheaper and more efficient in a form of institutionalized education that operates on transactions rather than intellectual growth.
STUDENT-CENTERED & INQUIRY-BASED
How is your class student-centered and inquiry-based? The committee would want evidence that your class is not exclusively stand and deliver passing on of content expertise, but that you are constructing problems ahead of time and guiding them toward solutions.
I’ve written about my commitment to student-centered and inquiry based learning at several points in these pages, particularly in my description of profession development at U. Penn’s Project-Based Learning Certificate Program, my implementation of the CPM curriculum, and my transition to Criterion Based Grading. So in this space, I would like to share a random sample lesson problem set and describe the lesson plan as intended for students to learn by doing the problems.
This is a problem set for the first lesson on a unit teaching the PreCalc* topic of Sequences and Series. Students will be introduced to the definition of a Sequence as an arrangement of numbers that progresses in order according to some pattern. Students will learn that the arithmetic operations that produce each number in the sequence can be calculated using a formula in which the input is the term number (which place the number appears in the sequence) and the output is the sequence term value (the value of the number itself).
In problem #1, students are given 10 different sequences, without being told anything else about them. They are to investigate the nature of sequences according to an iterative process by which 1) they identify the pattern for each sequence so that they can accurately predict the next three values, 2) recording the term numbers and the term values in a table, 3) plotting the data from these tables on an x-y coordinate plane, 4) writing a formula that would generate the value for any term number so that students can predict what the 100th or 1000th term in the sequence would be without using the pattern to calculate all of the proceeding values.
While students are working collaboratively on these tasks, the teacher moves around the class observing and facilitating teamwork dynamics, framing the learning by asking scaffolding questions, and noting aspects of the topic that might need to be explained further via alternative instruction models.
At the completion of problem 1, the teacher will draw all the students together in a whole class conversation to ask the students what the main takeaway ideas were, synthesize and direct their contributions according to the lesson objectives, and engage the students in open discussion about moments of wonder or discovery.
The remainder of the lesson is a series of problems created and/or resourced to give students opportunities to practice, deepen and or extend their thinking about the topic. The teacher resumes moving around the classroom noting the learning that is taking place and finding opportunities for clarification and extension. Helpful commentary is included in the margin to indicate to the students the nature of the problems and what is intended to be achieved. Also in the margins are pre-recorded direct instruction videos made by the teacher. It is not intended that students watch those videos during class time. Rather the intent is to prioritize interaction with their peers and teacher, but with the extended block schedule that may include asynchronous learning opportunities, some in-class time may offer an appropriate moment to take a few quiet minutes to access these videos for extra support.
The class concludes with a brief 5 minute reflection about the main ideas from the day and to prepare the students' thinking for the next lesson.
As you can see, the teacher spends very little, if any time directly “instructing” this particular lesson. Rather the teacher allows the students in their groups to dictate the pace and focus for how the learning is to be accomplished. The problems are written to illicit inquiry from the students. No answers are immediately obvious, nor is it necessarily obvious how to begin the solving process. The lesson explicitly makes “making sense of problems” one of the learning objectives and the teacher is supporting students to develop this important thinking skill as much as the mathematical content. The fact that the nature of the questions is rooted in inquiry differentiates the task in front of the students. The questions are “group-worthy” because learning is optimized not just by having a computational whiz kid who can accurately compute the problem in a matter of minutes. Instead, learning is optimized by having groups with a student who can reflect on the nature of the problem asked, a student who can make sure all voices are heard, a student who can make creative connections between mathematical representations, a student who can communicate the group’s findings intelligently, a student who can organize the resources of the task, and others, all in addition to a student who excels at computation.
This, I believe, is what student-centered, inquiry based learning looks like. It puts the students at the center of the learning and the learning is driven by inquiry. It is fundamentally a space that all students see themselves in, and from which they derive the enjoyment of stimulating their intellectual curiosity.
SCHOOL INITIATIVES
Describe how you have responded to and formally implemented school initiatives, including but not necessarily limited to decision education, curriculum mapping, global readiness, diversity, etc.
The most pressing school initiative I am involved in at the moment is responding to Headmaster Dr. John Nagl’s call to practice anti-racist teaching, learning and policy making in our Haverford community. In the wake of the murders of Ahmaud Arbery, Breonna Taylor and George Floyd in the Spring 2020, after multiple moments of student leadership such as Jackson Overton-Clark’s documentary Black at Haverford in the months and years before, administration, teachers, staff, alumni, parents and students all called for careful reflection and examination of the racist policies and practices perpetuated at Haverford in its history. I was already engaged in leading reading groups before the Spring 2020, but now there is renewed energy to translate reading and reflection into action, so I am helping to spearhead the establishment of a BARWE (Building AntiRacist White Educators) chapter at Haverford. This group will welcome all educators at Haverford, but will conduct a self-analysis of race in education through the white teaching lens. The intent of this group will be to balance intellectual engagement around articles and discussion with actionable goals designed around elevating the agenda and voices of our student-led diversity and affinity groups such as the Diversity Alliance. There have been many calls for the creation of a SEED 2.0 at Haverford and the plan is for this BARWE chapter to be one of several options educators can engage in to further their anti-racist teaching practices and policies.
Another school initiative I have engaged fellow teachers in is with the analysis of MAP data in our middle and lower school. At a previous school, I served as the lead MAP Data Analyst in which my job was to support teachers, parents and students in making sense of the resulting data from MAP Testing. I have now met several times with my LS and MS colleagues, examined the data from their classes and made recommendations on how to craft a narrative from the data. The implementation of the new Lower School Math Curriculum, ORIGO, should provide an ideal opportunity to dig deeper into the MAP data to analyze the results of using this really interesting curriculum.
In leading a group of students to the beautiful country of Morocco during the summer of 2019, I helped forward the school initiative of global studies. Mr. Andrew Poolman invited me to participate in this opportunity particularly to leverage my prior experience living and teaching in Morocco with my family, and sure enough, I found that I was able to uniquely support the students’ study travel experience in a number of ways. I had an amazing time inviting students to try the various Moroccan medina cuisine, helping them to negotiate the social interactions, recalling stories of my experiences during my time living in the country and of course being a source of emotional support as they navigated the complex range of feelings they were experiencing. The trip was prefaced by a series of club sessions in the Spring of 2019, which gave me a great opportunity to get to know the students better and learn about their expectations and goals for the trip. I was able happy to continue my involvement with Mr. Poolman's global studies projects by contributing to his Global Studies course on Cuba by being a guest lecturer on the topics of data analysis to support the students in crafting their funding proposals.
Finally, and this was an opportunity I cited in an earlier response but I would like to mention here as well, my time running Haverford’s Intellectual Curiosity Day resonates with me as one of my favorite Haverford initiatives, and I look forward to continuing to lead this event in the future.
COMMUNITY CHALLENGES
Speak to a community challenge or opportunity which you have identified and "stepped up" in response to.
There are three community challenges that I either identified or that I was presented with and that I subsequently “stepped” up in response to.
Math Club
Rank Choice Voting
Inter-form Olympics
When I arrived at Haverford, the Math Department was already hosting a number of really amazing math opportunities for students beyond the class time spaces. Susan Mitchell was hosting a Math Madness event once a week in the morning with breakfast sandwiches. Newton’s Notebook, a magazine of student learning in Math and Science, was gaining popularity. Sam Walters was organizing a robust American Mathematics Competition (AMC) and taking teams of students to participate in the Temple Actuarial Sciences Math Competition. In the spring of Susan Mitchell’s departure from Haverford, she asked if I would take over the Math Madness event, which of course I accepted and in the process of organizing and observing the students participate, I began to notice that as fun and engaging as all these math events were, they were disparate, unconnected events that popped up on students’ radar from time to time. I realized that a cohort of math students was entering our community with a passion for more rigorous intellectual learning around mathematics and math contests. I noticed that there was a dearth of team contests and events. Finally, I saw that as much fun as the math contest problems were, most were disconnected from real world problem solving. So in response, I recruited a few students to develop with me the Math Club, that would house all these events, plus additional team contests such as the Purple Comet Contest and real world problem solving contests like Mathworks Modeling Challenge. The energy from our club grew and we developed the idea to customize the Arete Labs Math Madness online platform to build what we are now calling The Philadelphia Independent School math league. We invited our friends at Episcopal Academy, Baldwin, Shipley, Penn Charter amongst others and played out an 8 week league season that culminated in an in-person Olympiad at Haverford in the Fall of 2019. By all accounts, both the league and the olympiad were a success and every attempt will be made in the Fall 2020 to do it again.
After the student council elections for the 2019-2020 academic year, there was a call to reform the election process so that the student body president might reflect the preference of the greatest number of students, rather than the most popular. At the time, the student body president was chosen by the entire student body from a choice of 3 senior finalists, who were the three most popular candidates from a primary election amongst the seniors. The glitch in the process was that there was no restriction on the number of senior students who could put their name forward as candidates in that primary. So if 20 seniors put their name forward as candidates in the primary, and all approximately 120 seniors vote for one of those 20 candidates, then the three most popular seniors candidates could very well garner less than 20 votes each. If that was the case, that would mean half of all seniors would not have their candidate emerge from the primary. In short, there seemed to be a problem of legitimacy. I supported using a system of Rank Choice Voting, which many political theorists believe is the most democratic method of electing a leader, including no less than our very own Mr. Tim Lengel. In short, Rank Choice Voting allows students to order a select number of candidates according to their preference and as candidates are eliminated for having the least votes, or not having a viable mathematical path to winning, the students who voted for that eliminated candidate would have their vote recast for their next preferred candidate. It ensures every student’s voice counts and that a more diverse set of candidates might get consideration instead of merely the most popular. The challenge of course was devising a system for sorting, organizing and assigning votes, and for that I solicited the assistance of our talented students in the Software Programming course to write an application to perform the function for us. Rank Choice Voting is ideal for elections in which there is a large, diverse group of talented candidates, and for which students want to express the preference for their leadership. It has since been used for a number of purposes beyond student government including electing Honor Council members, Wrestling Captains, Honors Chemistry topic choices, and end of the year student awards. So in Rank Choice Voting, I responded to a question of legitimacy in the leaders our students elect and the decisions we make so that they reflect the greatest preferences of our community.
Finally, early in my first year at Haverford, I heard Form III advisors comment that the students wanted a way to build community within their grade during advisories. I thought it would be fun and a great way for advisees to make connections, to have a friendly contest in which Form III advisories would compete against each other in games and puzzles. With the Inter-Form Olympics Each Form III advisory would choose it’s “Home” game, whether it was a fast paced athletic affair such as dodgeball or handball, an intellectually rigorous match such as cards or trivia, a common party game such as corn hole or charades, or a zany off the wall idea such as “walk the plank” or library steal the bacon. I created the schedule and kept track of league standings, but really the students and other advisors brought the energy and enthusiasm for the events. I’m happy that it has become a traditional element of the Form III advisory program and I look forward to seeing where it goes in the future.
These three contributions range in the degree of impact, but I hope all demonstrate my commitment to identifying challenges within our community through conversations with students and colleagues, and working collaboratively to come up with solutions.
INVOLVEMENT IN WIDER COMMUNITY
In what ways have you worked with the wider community outside of your classroom? Been a team player with your colleagues, identified school problems with your colleagues and appropriately found solutions? Brought colleagues together, and used appropriate methods of problem solving with supervisors to bring about positive change?
Since the time I arrived at Haverford, I have attempted to take as many opportunities as I could to be involved in the wider community. Indeed, I see my job as an educator as one not confined to my subject matter and classroom space, but rather a teacher and coach of life lessons to young learners. Often time, experiences outside of the classroom present the best opportunities for such lessons. Additionally, Haverford has a history of rich traditions and in becoming a part of the community I resolved to learn as much as I could about them by participating and making connections within them. Here, briefly, are some reflections on such moments.
Since the beginning of my tenure at Haverford, I have been enormously impressed with the tradition of presenting a Reflection during a weekly assembly. Watching so many brilliant colleagues and students stand and talk about some personal aspect of their lives and learning from the connections they make between their lives and the current moment at Haverford has simply been inspiring. I have seen too many incredible Reflections to name them here, but I resolved early on that I would like to present one myself. I was not sure which topic to take up, but having planned the Philly Independent School Math Olympiad for a Tuesday in November, I decided to present a Reflection on the Monday prior about how I came to discover what mathematics was really about. In short, I had a fairly typical high school level understanding of mathematics in which I thought it was all about computations and formulas, until I completed degrees in Philosophy and then I realized the powerful intellectual thinking that defines the entire subject. I also welcomed on stage Tim Kelley from Aretelabs, which, as I have mentioned, produced the online platform for the Math League and Olympiad, to talk about entrepreneurship and math contests. If you would like to see my Reflection in full, you can find a link to it here.
I was equally intrigued by the “25 Things Every Man Should Know” series for seniors in May. In my first year at Haverford, I had my second child and Ms. Carmen Epstein had a baby as well, so we designed a session on “Baby Care” where the boys got to hold the babies, change diapers, mix and heat formula/milk and set up a pack-n-play. It was a lot of fun, certainly a one off for me, but I found the session I really wanted to work with to be Mr. Tom Tracano’s Ethics course. He graciously agreed to include me in his planning and in the first year, we used almost entirely his presentation from past years, sprinkled with a little more technical thinking from my educational background in Philosophy. The next year, he was busy pivoting to his new job in San Diego, so he turned the whole session over to me, and though I really enjoyed centering the conversation around the famous Trolly Car ethical dilemma, I really wanted to focus on dilemmas more real to the students’ lives. So I revamped the course using ethical dilemmas from life in college that I myself remembered, students reported hearing about, and that I researched from the Markkula Center for Applied Ethics at Santa Clara University. I believe this elevated the discussion and ethical inquiry to another level because the situations we spoke about were personal and students could relate to them in their own life. I have since led this “25 Things” course every spring, adapting it this past year to reflect the virtual learning and living environment we found ourselves in as a result of the coronavirus epidemic.
I briefly want to use this space to mention a few other experiences I have had working in the larger community, and they include being invited to participate in the Upper School Head Search for the 2018-2019 school year, contributing to Ms. Lisa Snyder’s Inquiry Group making Service Learning outside of the classroom a critical component of my Form III advisory curriculum such as annually participating in Shiverfest and leading a group to the Mitzvah Circle Foundation for The Day of Service, and annually chaperoning the Form III/IV Semi-Formal. Each of these experiences have helped me to create deep and lasting memories with the community.
PARENT PARTNERSHIPS
In what ways have you developed and maintained a built a partnership with parents? What specific things do you do to manage boundaries, expectations, communication?
Partnering with parents is one of the areas of Haverford where I am looking next to grow. I feel that now being at Haverford for 4 years, and seeing young men who I taught as Form III students matriculate into their Form VI year, has given me the opportunity to grow with the families in both academic and athletic contexts from when we met when we both arrived at Haverford until now. Indeed my own daughter having just completed kindergarten at her elementary school has given me a new perspective on the importance of forming partnerships between teachers and parents, I have committed myself to focusing more on this area of my work at Haverford. There is one area in which I believe I have initiated forming parent partnerships in the Classroom Newsletters, and one area that I aspire to form parent partnerships in the Parent SEED Program.
During the 2019-2020 school year, I began writing Classroom Newsletters home to parents having been inspired by my colleague in the math department, Ms. Barbara LaPenta, the year before. I found them to be a remarkable tool for keeping parents informed about the lessons and projects that were happening in the classroom, explain and justify class policy changes, provide general feedback to questions asked, and acknowledge accomplishments by the students. I received really positive responses from the parents thanking me for staying in touch and offering opportunities for their feedback. This was certainly a first step, but it was great for laying the groundwork for future correspondence.
Additionally, I aspire to be a faculty leader in the Parent SEED Program. I first became aware of Parent SEED last summer at the Race Institute workshop I attend with Ms. Sarah Barton. Then in the course of the Faculty SEED program, there was an evening in which the two SEED groups came together to have dinner and discuss. These conversations were inspirational and thought provoking and I decided that I wanted to take the work that I had started developing at Haverford into those spaces. My plan is to focus on launching the BARWE Chapter at Haverford, continuing to support the Reading Groups, be a continuing visiting member of the Faculty SEED Program and then participate in the SEED Leadership Training with the next two summers. Of course, this could change, but I am also inspired in my personal life to become trained in working with parents on topics of identity, equity and inclusion through my participation in my daughter’s elementary school parent diversity group. I am looking forward to future opportunities to develop my skills in this regard.