Relationship of Objectives, Assessment, and Instruction

We are asked to address if we think that the pyramid diagrammed above aptly displays the inter-dependent relationship between instruction, assessment, and learning goals (as written in the book, or content standards here...which in the current system is synonymous with learning goals). I agree with Brookhart that the model is a bit too simplistic to be carried too far, but the basic idea is good. One often things of the counter-clockwise path around the triangle -- learning goals --> instructions --> assessment. However, I like that this graphic reminds me that the learning goals should inform the assessment directly, too. For example, if I are wanting students to apply a mathematics topic but most of the questions I write are memory/recall, I have not assessed students based on the original goals. Additionally, I find it a good reminder that the assessment also returns to inform the instruction and the learning goals. It is not the end of the line of the students' learning. So, yes, I will keep this in mind as I think about assessing my students so that I know that my planning of their learning is inter-connected and balanced.

Pondering Grading

Through a couple of the other courses we're taking this semester, we've touched on the subject of grading and student assessment. It seems like a rather big deal. And I'm thankful that we're getting a chance to study it more deeply because it seems that student assessment needs a bit more thoughtfulness than printing off the exam given at the end of the chapter in the teacher edition of the book exhibits. Thus, I've been thinking a lot of late about some of the key concepts presented in the chapter--that there are better ways to serve students than the current practices, that grading needs to accurately and reliably communicate clearly about students' achievement of learning goals.

One thing I believe about grading that this introductory chapter didn't include is that I think there is a better way to grade that doesn't just assess the students' current achievement but also is the catalyst for more learning. I believe that there must be a method of assessing students that is more of a pivotal point in a conversation about their learning path, something they respond to and encourages their continuing growth, than it is a number at the end of the journey. At least, that's a dream of mine. I'm not all that familiar with what's out there.

Love's Labour's Lost - A Grading Story

Usually grades work in my favor, really. I'm a good student. I like learning. Teachers like me. I happen to test pretty well. Teachers give me good grades. We're all happy.

But there is one other time.

The spring of my junior year of college, I took 4 math and physics courses, 14 of my total credit hours. So, I took an acting class to balance out the semester. It was 5 credit hours because we met everyday to practice (i.e. distract me from my mental tension and give me a creative outlet), and it was considered one of my physical education courses. Score.

The course started well. We did some acting exercises which involved getting into all sorts of characters, we did some reading from an acting theory book and started to develop our raw talents. Then, the professor started periodically not showing up for class or just being extremely late rather frequently. I think she had something going on in her personal life, but in my college mind, this was an extreme breach of an unwritten academic contract, and I lost great amounts of respect for her.

We didn't do much for the rest of the semester, which culminated in a final project of participating in a play.  We all tried out for the university's spring productions, and if we were not cast in one of those roles, we were supposed to break into groups and act in a one-act play in front of the class. I was cast as Sir Nathaniel, the curate in the university's production of Love's Labour's Lost, a little-known Shakespeare comedy. If you're wondering about the casting choice, I shall inform your pondering mind. Yes, that is a male role. The special-guest director was trying to do that cool, modern cross-gender casting of Shakespeare plays. And I was playing a two-bit role of comic relief as a stupid yes-man with about 10 lines.

In Shakespearian style, there was a part in the play that was a play within a play in which Sir Nathaniel is playing Alexander the Great, so I spent a good portion of the play in a thin, belted silk shirt and tights, looking more like a Russian male figure skater than I'd ever like to admit to.

And the director wrote a special song to end the play. In which he had me sing a soprano solo. Now, I have spent a good portion of my life singing in choirs, so I can carry a tune, but if you have paid attention to my speaking voice, you have probably ascertained that I am solidly an alto. I basically sing tenor. Oh, and I sing in groups, not solo.

So, let's recap. This means that for two weeks, every night I stood in front of an audience, playing a male, in an embarrassing and revealing costume, and squeaking a solo at the end.

And then I went back to my room, put on sweatpants and hid from the world (and did math and physics homework) until the next night when I repeated the experience.

I have never been so publicly humiliated in my life.

And, finally, the coup d'état. The professor. Who had the gall to not show up to many of her own classes. Gave me a B for the class. Did I get a B in any of those math of physics courses? Nope. All A's. In fact, up until that point, I had a 4.0 average. But for the 5 hour acting class? B. When I asked why, she said that my performance in the play was uninspiring.

I have reviewed this scenario multiple times to see where I went wrong. Yes, I am sure my 10 lines containing no character development were uninspiring. I do hope they were somewhat funny. I am sure my attempt at a soprano squeak didn't leave her humming as she left the auditorium. But was there much that I could do better, given the situation? Was there something I did that was offensive so that the grading was retaliation? Maybe my attitude toward her class showed through, but really? Really?!

So, in the jargon of the chapter. I think both the validity and the reliability of the grading went wrong.

In this case, I hardly got a chance to act, so forming an entire semester's grade on my few lines and standing in the background on stage is like grading a student for the semester on their completion of one exercise. There's a whole lot to gain and loose in those few moments, and when the depth of the character the student is acting is minimal, can one grade them for character development? Which makes this assessment invalid.

And I am pretty sure that interpersonal or life circumstances got in the way of her grading decisions so that the grade I made on the day she submitted scores would not be consistent with the grade on other days and situations, making the scoring unreliable.

And all of this, made me really, really irritated. And I felt helpless and poorly-represented. And mad. To this day, I get mad about this. In fact, when I told my husband that we were supposed to reflect on a time in our lives when grading went wrong, he said, "oh no."

So, dear semi-anonymous internet counseling system, here is my story. Told one more time so that perhaps tomorrow I will get slightly less mad and learn from it.

Reflecting Upon My Own School Experiences

I had rather drastically different middle and high school experiences. I went to a little country school for K-8th grade (Lascassas Elementary). We're talking kids used to conjure up Bloody Mary and the Bell Witch of Tennessee (who was a relative of our librarian, she had a genealogy and non-fiction book about her in the library to prove it) during recess and then baptise themselves in the stream at the back of the playground. It was more of a middle-school setting because I graduated in a class of 60 and followed with the same class from 6-8th grade. Since there were so few students, we had very few extra programs, teams, and such. But it was also very personal.

We joined the city kids at one of the large public high school, Oakland High School, after graduating. I had a class of 470 when I graduated. At the time, there were only 2 public high schools in our town and they were extremely overcrowded. In the last 10 years, they have built 2 additional schools. The original two schools were rather diverse. They really just took the kids who came from the two sides of a large town which created two socioeconomically and racially diverse high schools, and I think that was helpful to me. Even though I took honors classes and roamed the halls rather clueless about what was going on in some of my peers' lives, I had glimpses of diversity, and it was good for me. With the addition of the 2 new schools, many of the best teachers from my high school experience left to go one of the new schools, and I have heard now that Oakland is now the "rough" school.

I was a really busy high schooler. I swam, sang in a choir, headed up one of the Christian organizations, took multiple instrument and voice lessons, was really active in my church, and did all of my homework. Perfectly. Because if you haven't noticed yet. I was an over-achiever. Thus, it wasn't unheard of for me to have a day that looked like this--

• 5:00 - swim practice
• 7:25 - meet with my best friend in the parking lot of the school and read. For fun. In her car. 
• 7:45 - school 
• 3:00 - swim practice
• 5:30 - cello lesson
• 6:30 - church activity
• 8:30 - homework
• 9:30 - bed. (Yes, I also went to bed at 9:30 as a high schooler.) 

As you may have gathered from my description of myself, I wasn't entirely "with it" as a teen. I was a bit of a geek. I was in a bubble of achievement, and I had no idea what other kids do after school until they went to bed after midnight. Additionally, I took pretty much entirely honors classes, music, and art, and so even my school time was spent in a bubble of achievement. I sat eating homemade salads and grilled chicken for lunch, and I have *no idea* what our cafeteria served, but I'm suspicious it wasn't salad and grilled chicken.

I remember many quirky teachers who in the end probably taught us well, but I don't have this grand-impact memory about most of them. In retrospect, I don't think I stood out to teachers. I think I was maybe uninterestingly studious. (The same held true for college.) While most people I know have a teacher who connected with them in some way and interested them in the subject matter or life in general, I never really had a teacher who seemed to care about me. So, there are a few whose classes I remember fondly because I liked the content myself or because I felt they taught particularly well - Mr. Gardner (8th grade Algebra), Mrs. Daniels (described in a previous post), Mrs. Frazier (French).

I would love to forget my Algebra 2 class, please. My memory of the teacher is that she was a terribly poor communicator. I don't know if she knew the Algebra 2 content or not, but whatever content she knew was lost in the distraction of her saying "coocolator" and speaking unclearly. Some students openly mocked her, I squirmed through class and wished the painful experience was over, for everyone involved. After that class, I remember taking the textbook home and reading it on my own and doing the exercises over the summer, making sure I had the content knowledge for my Trig/Pre-Calc class. Again, yes, I was that student.

I don't remember much peer or parental pressure. I think one would argue that if my sister and I were both so driven, we had to have had parental pressure, but if we did, it was masterfully subversive. I do remember wanting to have romantic interests and my parents refusing. But I didn't have any particular candidates banging at my door, so even if I wanted to, there was no opportunity to go behind their backs and make out or whatever anyway.

And I just didn't have time to have peer pressure. I do remember my date to prom wanting to kiss me, and I just wasn't into him, and so I started throwing my shoes at the ducks and chasing them to disperse some of the pressure. Smooth.

I think I felt undesirable and isolated. I knew subconsciously that I lived a different life from most of the people around me, and I watched crush after crush go and find more classic girlfriends. But I was also pretty happy and self-confident that I had my future interests in mind. Call it a swan-complex, but I knew that I was a bit awkward and undesirable to teens but that I was talented, smart, and driven and I could make it in the world at large. I also had several good friends and didn't really want from activity. It kept me out of trouble.

Continuing to hone my philosophy of teaching...

I haven't made so many edits to this version, to be honest, as I feel it's getting closer to what I want to communicate about myself at this stage of life so I don't have that much to change about it.

Invention and Investigation in Mathematics

Many students associate math instruction with being taught a trick to finding the right answer to problems. I was lost in this trick-wielding arithmetic I learned as a child until later when I understood how to think critically and reason about the structure of mathematical systems. In fact, as a high-school student, I often came home from school wondering why the geometry or calculus methods I was learning in school worked, and I would methodically reason out and prove them to myself. It wasn’t until I received college-level coursework that I discovered the intriguing world of logic and abstract ideas behind the arithmetic we use, and it thrilled me. While I was working with the Educational Program for Gifted Youth at Stanford University, I discovered that their curriculum introduced students to logic and reasoning in the 2^nd grade, and I found that what I suspected was true: math facts and tricks stick better with students when they better understand the basis for their usage. I enjoyed watching students catch onto the excitement I have for math at a younger age as well.

Due to my personal experience in learning and teaching online, I believe students will gain more from their mathematics instruction with a more investigative approach than the usual lecture and homework problems. I will rethink the traditional instruction I’ve received before I pass it on to students in order to ensure that they learn how to think critically and mathematically about a problem. The key to a mathematical problem is not the answer but the thinking process that produces the answer. I must draw on the methods of teachers in other content areas and then ask myself, “That was a literature course, but how can I apply the same fervor to mathematics?” “What is it specifically in mathematics that I find inspiring?” “How do you teach the beauty of abstract reasoning to students?” “How do I create adeep, investigative learning to motivate their minds?”

A key to teaching students a new method of understanding mathematics is an open environment, a place where no question is unwelcome; rather, curiosity is encouraged. Students are too familiar with fact-regurgitation mathematics in which they are “right “ or “wrong” which stifles many students’ ingenuity. I see my role as a teacher to retrain students to explore mathematics and help them hone their thinking skills and creativity so that they can experience the excitement of discovery, that fabulous “Eureka!” moment of an epiphany when they feel they truly own a new concept. I will create a motivating classroom environment by introducing new material with enthusiasm, encouraging students to explore the familiar material by asking them diverse questions, requiring them to write about their thinking processes as they work problems, and answering their inquiries by modeling the sort of openness and investigative spirit I hope to see from them.

I was brought into teaching because I am myself always hungry to learn more, and I would like to help my students to continue to grow and explore as they mature through adolescence. I will exemplify the professionalism (timeliness, respectfulness, organization and planning, integrity) that students will need to succeed in their academic, work, and personal life. Throughout my teaching career, I will remain open to learning and correction and continue to grow professionally. I want to continue to take courses to remain up-to-date in relevant topics and discoveries in mathematics and education and to keep myself exploring and creative in my instructional techniques.

Teaching Philosophy

I hate doing things that I am bad at. I hate even more doing things where I feel uninformed and doomed to badness. How does one go about writing a teaching philosophy for student teaching applications when one is 4 weeks into deciding to be a teacher? How in the world do I know how I'll conduct my classroom or what overarching themes will guide my instruction, student relationships, and classroom management? I feel awfully green and clueless.

What do I know about teaching? I know that I like math and physics. I know that I find them pristine and beautiful. I know that I think I might be able to transfer the information to students, possibly even well. I know that I am an empathetic and caring person who wants to be where I can enter into a person's experience and help them find wisdom and that that probably makes for a good teacher. I know that I feel like I lack the experience of a teacher that cares about me because perhaps math teachers don't tend to be the caring sort, and I could fill a void there. So, here we go. A sketch of my teaching philosophy.

Invention and Investigation in Mathematics

Many students associate math instruction with being taught a trick to finding the right answer to problems. I was lost in this trick-wielding arithmetic I learned as a child until later when I understood how to think critically and reason about the structure of mathematical systems. In fact, as a high-school student, I often came home from school wondering why the geometry or calculus methods I was learning in school worked, and I would methodically reason out and prove them to myself. It wasn’t until I received college-level coursework that I discovered the intriguing world of logic and abstract ideas behind the arithmetic we use, and it thrilled me. While I was working with the Educational Program for Gifted Youth at Stanford University, I discovered that their curriculum introduced students to logic and reasoning at a much younger age (2^nd grade), and I found that what I suspected was true – the math facts and tricks stuck better with students when they better understood the basis for their usage. I enjoyed watching students catch onto the excitement I have for math at a younger age as well.

Due to my personal experience in learning and teaching online, I believe students will gain more from their mathematics instruction with a more investigative approach than the usual lecture and homework problems. I will rethink the traditional instruction I’ve received before I pass it on to students in order to ensure that they learn how to think critically and mathematically about a problem. The key to a mathematical problem is not the answer but the thinking process that produces the answer. I must draw on the methods of teachers in other content areas and then ask myself, “That was a literature course, but how can I apply the same fervor to mathematics?” “What is it specifically in mathematics that I find inspiring?” “How do you teach the beauty of abstract reasoning to students?” “How do I create a deep, investigative learning to motivate their minds?”

A key to teaching students a new method of understanding mathematics is an open environment, a place where no question is too stupid to ask; rather, curiosity is encouraged. Students are too familiar with the fact-regurgitation mathematics in which they are “right “ or “wrong” which stifles many students’ ingenuity. I see my role as a teacher to retrain students to explore mathematics and help them hone their thinking skills and creativity so that they can experience the excitement of discovery, that fabulous “Eureka!” moment of an epiphany when they feel that they truly have a handle on the concept as their own. I will attain a motivating classroom environment by introducing new material with enthusiasm, encouraging the students to explore the familiar material by asking them diverse questionds, requiring them to write about their thinking processes as they work problems, and answering their enquiries by modeling the sort of openness and investigative spirit I hope to see from them.

I was brought into teaching because I am myself an incorrigible student, and I would like to help my students to continue to grow and explore as they mature through adolescence. I will to exemplify the professionalism (timeliness, respectfulness, organization and planning, integrity) that students will need to succeed in their academic, work and personal life. Through my teaching experience, I will remain open to learning and correction and continue to grow professionally throughout my career. I want to continue to take courses to remain up-to-date in relevant topics and discoveries in mathematics and education and to keep myself exploring and creative in my instructional techniques.

Experience 6.2 - Student-Centered Instructional Activities

Reflecting on my past involvement with student-centered instructional activities

Brainstorming - F, E
Buzz session
Case study - F
Committee
Cooperative learning - F
Debate - F
Discovery - F, E, L
Discussion,whole-class - F, E, L
Field trip - F, E, L
Fishbowl
Forum
Inquiry - F
Jury trial - F, E, L
Learning activity center - F
Panel discussion
Project or independent study - F, E
Role-playing - F, E, L
Roundtable discussion - F, E, L
Simulation - F, E, L
Sociodrama -F
Symposium

"F" for Familiar with
"E" for Effectively used.
"L" for Liked

Exercise 6.1 - Direct Experience Learning

Nearly the entirety of my high school physics course was taught by experiment/direct experience. The teacher, Mrs. Daniels, had us do daily experiments to discover the principles of mechanics, optics, etc. We would regroup and summarize periodically, but most of the instruction was experientially-based.

We would come in every day with our graphing calculators, she would give us worksheets of instructions and charts and tables, and we'd get to work and set up experiments with motorized carts or colored lights and take data. We would graph or chart our findings and draw conclusions. Then, we would discuss our experiences as a class and share our data, and Mrs. Daniels would supply the formal forms of the theories we had studied.

I think I remember this particular class because it is very unique to have such complicated material presented almost completely through access mode teaching. This is also one of the few direct experience experiences in math or science that I can remember liking. In high school, I remember finding exploratory tasks in math and science "light", rather lacking in content. However, in this case, I really enjoyed the thrill of figuring out how acceleration and velocity were directional. I remember the moment that the I figured out why the acceleration graphs of something speeding up toward me or slowing down away from me looked similar, and that moment was full of the intrinsic motivation teachers hope for. 

I also remember her first test was the first time I ever got a low-end B and it was shocking! That definitely lit a fire under me and taught me how to study!

However, I would have to admit that the course somewhat poorly prepared me for college-level physics courses. While it did teach me content in a personal and rememberable way, it didn't drill into me the hard-core knowledge I was going to need for higher-level study. But, I suppose I made it in the end through many an upper-level physics course, so maybe it wasn't so lacking afterall....