Brian+Carreon

UNIT DESIGN


 * Unit Design**: Applications of derivatives [[file:carreon, brian3.docx]]
 * Additional resource** [|lesson plans applications of derivatives.pptx]

For providing **//feedback,//** please click here

RESOURCE JOURNAL LINKS

Response Journal 1. click here Response Journal 2. click here Response Journal 3. click here Response Journal 4. click here Response Journal 5. click here Response Journal 6. click here

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__**Response Journal 1**__  ======

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 My name is Brian Carreon, and I teach pre-Calculus and Calculus at Dhahran High School. The majority of my students are very eager, very capable 16 to 18 year-olds who succeed in making my job very easy. ======

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 I am guided by 4 main principles in my approach to teaching. ======



 * ======Students benefit most from learning the discipline of calculus (and mathematics in general) for its //own intrinsic purpose and value//.  ======
 * ======Students must focus on //rigorous methodology and meticulous execution// so that true flexibility of skills and idea execution can be completed.  ======
 * ======<span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block">Students must focus on the //communication of their ideas and conclusions//, and improve the clarity of these communications.  ======
 * ======<span style="background-color: rgb(251, 249, 249)"><span style="color: rgb(0, 21, 158)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block">//Emotional and psychological development// and awareness are integrally tied to academic learning and students benefit from an overt emphasis on these developments within the academic environment.  ======

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<span style="background-color: rgb(251, 249, 249)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"> I am very eager regarding edf608 and its possibilities for improving my teaching skills and knowledge. I have come to recognize two weaknesses in my approach to assessment within my classroom. ======

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 * ======<span style="background-color: rgb(251, 249, 249)"><span style="color: rgb(17, 24, 167)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block">Students do not sufficiently own the outcomes or design of their assessment. Students need more awareness of the purpose and design of each assessment in order to facilitate faster skill improvement. Within my classroom, I have improved student awareness of purpose and objectives. I also communicate gestalt purpose-based ideas to my students, but most of this communication is oral and informal. The developmental capabilities of the age-group I teach forces me to allow them more ownership of the intent and design of their learning. More clearly, I must facilitate the separation of myself from the material I instruct.  ======
 * ======<span style="background-color: rgb(251, 249, 249)"><span style="color: rgb(17, 24, 167)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block">The assessments I design require variety, both in terms of presentation and format; in addition, these varieties require purposeful variety so students improve their abilities to succeed within the assessment framework of my classroom. The rigidity and timing of our school-schedule mandate that routines and assessments within the classroom be fluid and systematically simple. I have allowed myself, however, to become too rigid, mundane, even boring in approach to instruction and assessment. Students have continually called for more variety in my classroom. Variety of assessment, and student ownership of this assessment, is a valid and approachable way to facilitate this need. It is clear that this course, edf608, will improve my abilities within these two arenas.  ======

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<span style="background-color: rgb(251, 249, 249)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"> Within the specific domain of edf608, I have only two expectations. ======

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 * ======<span style="background-color: rgb(251, 249, 249)"><span style="color: rgb(17, 24, 167)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block">The execution of the assignments should be purposeful, clear, and effective. I am taking this masters course in order to grow as a teacher. I do not value esoteric or theoretical production too highly within this realm. I expect the results of this course to directly impact and improve student learning within my classroom.  ======
 * ======<span style="background-color: rgb(251, 249, 249)"><span style="color: rgb(17, 24, 167)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block">My other expectation focuses on the presentation and format within the course. I expect communication, format of assignments, and technology to be fluid and correct. I am very excited about the wiki-format of this course and the design of the course home page. I expect this instrument (an internet-based, wiki-based online course) to be an effective and clear tool to benefit my mastery of the course purposes.  ======

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<span style="background-color: rgb(251, 249, 249)"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"> <span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"> ======

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<span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"> <span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"> ======

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<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"><span style="color: rgb(173, 52, 52)">__**Response Journal 2**__  ======

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 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(30, 21, 188)">The author is typical of researchers of education in the following unfortunate way: <span style="color: rgb(249, 21, 21)">//he views the current institution of education negatively and lacking//. His initial report card on the knowledge arts points to very poor 'grades' on our collective performance. This is very unfortunate (I will discuss this further below). ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(27, 31, 182)">In addition, like many researchers, the author has developed his own (if useful) framework for continual instructional development which he calls Teaching for Understanding. This framework, which focuses on the improvement of student abilities within the predefined knowledge arts is a valid framework for improving student-learning. This framework definition, however, is not innovative nor productive in this realm. <span style="color: rgb(245, 10, 10)">//For many years teachers have been aware, explicitly or implicitly, of the different ways and different levels within which students learn.// What the author calls and identifies as Teaching for Understanding is simply a clarification of the higher levels of the learning pyramid put forth by earlier researchers. The author is simply redefining the educational wheel. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(27, 31, 182)">This redefinition is not purposeless, however, if <span style="color: rgb(245, 20, 20)">//particular educators can use this theory in order to improve student learning.// But awareness of this theory nor execution of its purpose is necessary in any education-based arena. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(27, 31, 182)">Finally, to come back to a previous point, the author's overall negative view of the culture of education is disheartening. Education works. Students learn. The bottom line must not be to criticize its performance, but to focus on our higher-level successes and help all teachers use these best-practices in better and more effective ways. I understand this most likely coincides with the authors purpose as well. He could, however, frame his paper in this way and <span style="color: rgb(249, 21, 21)">//a////void the negativity and stigma that is, unfortunately, all too common with educational research and communication.//  ======

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 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(27, 31, 182)">For teachers, who are all curriculum designers, the implications of this theory are nonetheless important. In my mind, the author is basically calling for thorough preparation and dissemination of the purpose of lessons and assessments to everyone involved, particularly students. //<span style="color: rgb(250, 10, 10)">Reflecting on teaching must be done within, around, and across classrooms in order to make learning more productive and purposeful. // ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(27, 31, 182)">There is one danger to this approach: //<span style="color: rgb(247, 34, 34)">different cultures, schools, and age-groups require specifically different skills and plans. //The execution of teaching knowledge arts must be allowed to exist as it best suits each classroom, within the overall guidance of its specific audience, and not necessarily within this authors' specific point of view. ======

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<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"> <span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif">**Responses to Preparing for Today and Tomorrow** ======

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 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(26, 19, 124)">"What I desire is an education process that is genuinely meaningful to students, challenging them with problems and ideas that they find both interesting and intellectually demanding. I want to assess that process by the depth of its engagement in students' lives." <span style="color: rgb(245, 10, 10)">//In substance and purpose, I wholeheartedly agree with the Mr. Eisner's above-stated thesis statement.// ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(26, 19, 124)">The author directly continues to explain his perspective by discussing "a number of aims that I embrace as being appropriate for our schools." He says that, in short; students must judge the strength and validity of ideas more explicity, students must develop critical thinking skills, students must develop diverse and meaningful literacy, and finally, students must effectively work together and own the process and outcomes of their own learning. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(26, 19, 124)">If one were able to construe the author's purpose of mere reflection or exposition, the presentation of the ideas would retain import. <span style="color: rgb(251, 35, 35)">However, //Mr Eisner's objectives are much more directed towards a representation of inaction and misdirection of the education system.<span style="color: rgb(45, 114, 251)"> // <span style="color: rgb(26, 19, 124)"><span style="color: rgb(45, 114, 251)"><span style="color: rgb(73, 79, 248)"><span style="color: rgb(251, 35, 35)">T  his objective is inappropriate and unfortunate, for reasons I have stated above regarding "//Knowledge Alive//."  ======

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 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(26, 19, 124)">Nevertheless, in concentrating on the theoretical framework of personal improvement on educational methodolgies, Mr. Eisner's framework <span style="color: rgb(246, 14, 14)">//fits very well with my own reflection and self-attempts at improvement within my classroom.// <span style="color: rgb(26, 19, 124)">In our school district, we use the Charlotte Danielson tool for teacher and staff based evaluations. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(26, 19, 124)">As a method of self-reflection, I have found that model to be a motivating and enlightening factor in my professional development. I have //<span style="color: rgb(26, 19, 124)">recognized <span style="color: rgb(245, 20, 20)">two key weaknesses // <span style="color: rgb(26, 19, 124)">in my classrom that clearly Eisner's aims; furthermore, I identified these weaknesses using the Danielson model. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif">T<span style="color: rgb(26, 19, 124)">he first weakness is that, using Eisner's language, that //my students must focus on meaningful literacy// <span style="color: rgb(26, 19, 124)">even within the realm of higher level high school mathematics. One the the key skills of the AP Calculus exam that students must develop through a rigorous process is the mathematical communcation of ideas and conclusions. Luckily, I can use both pre-calculus and calculus to develop this skill over two years, but it has taken a recognized need for this improvement. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(26, 19, 124)">Second, I believe that students will <span style="color: rgb(250, 10, 10)">//own the outcomes of their learning more meaningfully if they work collaboratively// <span style="color: rgb(26, 19, 124)">and effectively, self-reflect and assess, and finally own and master basic classroom procedures. ======

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 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(30, 24, 247)">I have only one other addition. I believe that within and across teacher-groups, rather than individual classroom outcomes, must become the focus of Eisner's stated purpose. This may be a department or other vaious autonomous and self-directed teacher committees. I believe that a <span style="color: rgb(252, 44, 44)">//wider view of student growth must be allowed to exist within and across disciplines.// ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(5, 23, 214)">Personally, I am very lucky. I teach at an effective, productive, and dynamic international school. Further, I work within a very professional and very productive math department. We have collectively initiated new classes, increased enrollment, increased AP enrollment, and increased all standardized test score results. We need only //<span style="color: rgb(251, 50, 50)">more autonomy-developing direction and responsibility across disciplines // <span style="color: rgb(5, 23, 214)">that we really and effectively can communicate regarding the validity of our approach to Eisner's aims. ======
 * ======<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="color: rgb(5, 23, 214)">Let me clarify. Teachers need only the time and allowance of responsibility to best develop the aims in their students. This time must include an effective professional development model as well as a philosophy of educational outcomes. But, teachers will succeed if given the right opportunities and general best practice-based environmental structures. Given the resources, class sizes, self-direction, professional development, and authority, the <span style="color: rgb(250, 20, 20)">//majority of our teachers already want to do more for their students.// ======

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<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif"><span style="font-family: 'Trebuchet MS',Helvetica,sans-serif"><span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">//__Benefits of constructivism__//  ======

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 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif"><span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">The website clearly articulates the key principles of constructivism. They state the the guiding principles are to "pose problems of emerging relevance to students, structure learning around primary concepts, seek and value students' points of view, adapt instruction to address student suppositions, and assess student learning in the context of teaching." ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">I think it is important to remember that //**constructivism is primarily a theory of learning, not instruction.**// Piaget and the other core theorists where the primary developmental theorists. It is important to view the students as constructors of knowledge, and teachers as facilitators of those creations. ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">Furthermore, I believe that many teachers are already great constructivists, and we can best serve our fellow professionals and our students by //**adapting current practices to appreciate and understand a constructivist perspective**// rather than label those that are unaware of this theory as basic and mundane traditionalists. ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">I appreciate one specific benefit within this view of instructional design theory. Taken as a whole, teachers and teacher groups will be encouraged to purposefully reflect on the interactions within and across classrooms. //**These interactions must include lecture-specific questions that are directed to and from multiple audiences.**// ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">If we are constantly asking students to construct their whole learned selves, and asking ourselves as teachers how we facilitate this process, then we will be seeking better method and best practices out amongst each other and communicating about learning. This is a //**great model for improvement of student learning within small, outcome-specific arenas**// such as departments or teacher teams. ======

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 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">My criticism of constructivism is its //**overt contrast and seeming opposition to what they call traditional education.**// There becomes specific moments in time where students simply benefit from all types of learning. Evaluation, critical thinking, general inquiry are important cognitive skills, but they are not the only ones that need to be developed within the classroom, and not all lessons, units, or even entire classes could or should focus on these in order to be most effective. ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">Within the framework of Bloom's taxonomy, knowledge and comprehension (the levels the authors point to as exemplars of the so-called traditional method) are the lowest levels. Within another framework, //**the development of knowledge and comprehension are the building blocks**// for the higher levels of application, synthesis, etc. ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">Students benefit most from //**teachers collectively and actively directing student learning towards the upper levels of the pyramid using a constructivist framework**// for their learning, not focusing on their own personal teaching methods as for constructivist thought. ======
 * ======<span style="font-family: 'Trebuchet MS',Helvetica,sans-serif">Teachers can acheive the guiding principles of constructivism by more //**effectivly communicating about the purpose and outcomes of their lessons,**// and openly questioning, inside and outside the classroom, the overall purpose of each lesson. ======

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<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"><span style="color: rgb(173, 52, 52)">  ======

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<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"><span style="color: rgb(173, 52, 52)">Response Journal 4  ======
 * 1) // **Personal meaning:** I am lucky in that most students are able to see the indirect path by which the subjects I teach are personally important and therefore create intrinsic importance in the material. First, I teach many students who plan to continue into technology, engineering, and other sciences. Second, families as a culture view mathematics as an integral part of their possible future successes. Finally, my students discuss how they see meaning in my lessons because the skills and knowledge will make university-level mathematics much more master able. //
 * 2) // **Accepting challenge:** Pre-calculus and calculus are difficult subjects for anyone, and particularly difficult for students at this developmental stage, where formal reasoning is only beginning to be examined, and students still lack clarity and organization in cognitive self-awareness. I like to daily assess the perceived difficulty of homework, lessons, or assessments. The student will judge, on a scale of one to five, by raising their hand, and indicating with their fingers, their own perceived difficulty of the ideas presented. I think that this helps them own more of their improvement through difficult ideas and assessments. In addition, students get accustomed to the idea that they aren't expected to be perfect; rather, I think it allows them to accept challenges as a process rather than an outcome. //
 * 3) // **Developmentally appropriate:** the skills of functions and their analyses are perfect for challenging the teenage mind given the right execution. Students view the important skills of analyses of functions and their related rates of change (pre-calculus and // // calculus) as difficult but controllable, esoteric but nonetheless important. //
 * 4) **Control:** // I have been able to provide examples of how students can use various technological outputs for their own learning, and try and adapt the curriculum of the course around specific objectives. I plan calculator-based interactions for students to explore this machine, as it readily invites them to learn in a new way. I demonstrate Google searches and how to navigate to good results. I have also demonstrated the use of the textbook CD-rom, the textbook websites, my own delicious page. In addition, I am always outlining resources within the textbook that I do not use and how they might attempt to master the topic independently through the text. Overall however, I would have to say that this is a weakness of my teaching style. //
 * 5) **Use of pre-existing knowledge and skills:** // This year, I redesigned the pre-calculus course syllabus to better streamline the curriculum and enhance our tapping of students' most recently acquired knowledge and skills. We are starting with trigonometry this year for three reasons. One, Algebra II ends with a basic trigonometric unit. Second, trigonometric skills have been too weak for students moving into calculus. Third, students better understand the purpose and challenge of the pre-calculus course by doing trigonometry first. //
 * 6) **Social interaction:** // One of my more rigid classroom procedures is the “Warm Up.” Students must be working on a prescribed activity before class begins in order to be receiving full credit. One activity involves the students purposefully reviewing the answers to the homework among themselves. In addition, at the end of lessons, using the above-described rating system, students reflect amongst themselves about the difficult parts of the lesson. //
 * 7) // **Helpful feedback:** I believe that frequent and purposeful feedback is very helpful if students can improve on later skill development. I think I help my students very effectively by providing regular and frequent feedback on their work. My students are constantly being evaluated, and I really focus on quick feedback so students own the results and look to improve. In addition, I have shown my students how to interpret the marks and point system of quizzes and exams so they can personally reflect on their learning. //
 * 8) // **Use of strategies:** I like the idea that learning “tricks” and outlines for skills can enable mastery of higher level thinking skills in my class. In calculus, students understand that we are always using a three-pronged approach (analytical, numeric, and graphic) to their investigations. As time progresses, students become better at initiating learning through all three of these approaches. I like to give them small labs that investigate applied problems using high level skills. The AP free-response questions themselves become wonderful tools for these activities. //
 * 9) **Emotional climate:** // Math can be a bit dry and less dynamic than science, social studies, or even language classes. I like to use myself as an instrument for positivity in the classroom. I like to involve my students in my own emotions in an attempt to draw some emotion out from them. I share my frustrations about myself and them overtly and regularly.  //
 * 10) **Environmental support:** // I work hard on physical space, but this is a tremendous weakness of my classroom. My classroom is ugly. Procedures are neither smooth nor student-directed. The students do not do a great job of controlling the physical space. //



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<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif"><span style="font-size: 90%; font-family: Verdana,Geneva,sans-seri; text-align: left; display: block"><span style="color: rgb(173, 52, 52)">Response Journal 5 - Justification of the backward design philosophy as the best pedagogical practice for unit-curriculum design. ======

This is an interesting prompt. It assumes agreement with the premise that backward design is the best pedagogical practice. This is a grand claim, and the author of the reading did not make any research-based claim as such. Allow me also to consider the idea that strict 'backwardness' is just as restrictive as the traditional lesson-homework-assessment structure of the majority of curricular planning.

There is one thing that is clear: careful unit creation and revision backward by design enriches the an individual teacher's ability to accurately, efficiently, and clearly evaluate student progress through content and skills. In addition, it is also clear that student learning may actually increase within an individual teacher's classroom over time; this increase in student learning is the ultimate prize when considering individual teacher's progress and is most likely directly linked with the reflection and revision that is built into the backward design process. As I move through the UbD unit creation process, it is also evident to me that I already implicitly use a backward process. I am constantly thinking about the big ideas, the end result, and different ways students can show progress in skills. I do not, however, explicitly identify for myself or my students these considerations as I begin or they begin with the lessons within a particular unit. It is this increase in clarity and communication that make backward design so beneficial.

I tend to view my own curricular movements as circular. I work through small ideas on my way to the bigger, more important ones in a variety of ways. Allow me to create the following analogy: Most of the time, it is important to be able to see the forest through the trees, but there are times when an individual, distinctly unique and important tree loses loses something if one focuses entirely on the forest. I also understand the need to call the UbD design process backward, as it accurately and poignantly draws attention to a change in methodology for curriculum design.

Within higher level mathematics, there are small, 'less important' ideas and skills that do not readily transfer or assist other topics or skills. These hidden trees, however, become crucial supporters for bigger ideas that one may encounter in higher level engineering, physics, chemistry, or computer science courses. It would be remiss of me to leave them out of the unit, and I might be apt to do that if my entire focus is always on the end, on the big picture. There is merit in the forward-thinking curricular design, and UbD must allow its users to initiate revisions to their units from any direction.

<span style="color: rgb(30, 159, 59)">Response Journal 6 - Behaviors associated with understanding. Knowing and doing VERSUS Understanding.

The creation of this unit has really made me reflect on the above questions within a novel arena of my own teaching. My unit-of-choice was for my AP BC Calculus class, an extremely rigorous, energetic, fast-paced high school course. The restrictions, guidelines, checks-and-balances, and actual exam format of the AP BC exam demand that I reflect constantly on the best pedagogical practices for these students. In addition, these students demand, appreciate, and create fun and energetic learning activities. They constantly and independently review and discuss the in-class activities as well as the homework. I doubt the two things exist together by coincidence. I see the behaviors of these students "understanding" all the time. They belt out answers, verbally and energetically anticipate my own verbal questions or answers. They probe in ways that probe theories and 'bid-ideas.' One can daily observe smiles, frowns, nods, head-shakes, and claps that reflect true learning. If you look really closely you can see the light bulbs not only flashing but exploding.

This awesome learning environment is contrasted, for me, by my pre-Calculus classes. I have been teaching this class for 7 years now. And each year I try and make major changes to the curriculum to improve student knowledge AND understanding, which I feel have equal importance in this comprehensive and coalescing course. I have not had the benefit of the backbone of the AP exam (though I am exploring how the AP prescribes the creation of this vertical team) and I have not as easily been able to see how to focus on understanding within this course. And this difficulty is certainly reflected in my students' overt behaviors. They do not ask as many questions. They are not as personally engaged. They sit and rest rather than participate and interact. I must accept responsibility for this. This fact was again reflected in my student evaluations. They expressed that they know the class is important, but they are not interested or invested in the material. This is sad. There is hope, though, through my processes here in the class. I am already making changes to have units reflect more backward design components and I will definitely include more authentic tasks for this precalculus class in the second semester.



<span style="font-family: 'Lucida Sans Unicode','Lucida Grande',sans-serif; color: rgb(110, 41, 194)">Feedback

 * **Stage 1 - Identify Desired Results** || Extensively || Somewhat || Minimally ||
 * **//To what extent are the targeted understandings...//**
 * Big ideas at the heart of the discipline (as opposed to basic facts and skills) in need of //uncoverage?//
 * Based on appropriate established goals (standards, benchmarks,sylabus)? <span style="font-size: 10pt; font-family: 'Arial','sans-serif'">
 * Targeted understandings framed by questions that spark meaningful connections, provoke genuine inquiry and deep thought?
 * Framed by provocative //essential// and //unit// questions?
 * Related to identified skills which are valid and relevant? ||  ||   ||   ||
 * **Stage 2 - Determine Acceptable Evidence** ||  ||   ||   ||
 * **//To what extent are...//**
 * Students asked to demonstrate their understanding through authentic performance tasks?
 * Appropriate criterion-based scoring tools used to evaluate student products and performances
 * A variety of appropriate assessment formats used?
 * Assessments used as feedback for students and teachers, as well as for evaluation?
 * Students encouraged to self-assess<span style="font-size: 10pt; font-family: 'Calibri','sans-serif'"> ||  ||   ||   ||
 * **Stage 3 - Plan Learning Experiences and Instruction** ||  ||   ||   ||
 * **//To what extent will...//**
 * Students know //where// they're going (the learning goals) and //why// the material is important, and //what is required of them// (in terms of unit goals, performance requirements, and evaluative criteria)?
 * Students be hooked and //engaged// in digging into the big ideas of the unit (through inquiry, research, problem solving, and experimentation)?
 * Students receive explicit instruction on the knowledge and skills needed to //equip// them for the required performances?
 * Students have opportunities to //rehearse//, //revise//, and //refine// their work based on feedback?
 * <span style="font-size: 10pt; font-family: 'Calibri','sans-serif'">Students //self-assess// and set goals prior to the conclusion of the unit? ||  ||   ||   ||
 * <span style="font-size: 10pt; font-family: 'Calibri','sans-serif'">Students //self-assess// and set goals prior to the conclusion of the unit? ||  ||   ||   ||