MATHMark

7/27/11 Grading: What is one area of confidence AND one aspect I plan to develop or refine during this fall semester?"

Confidence: I think that I can assign authentic and meaningful homework and projects. I do not plan to assess the homework as part of the calculated grade, but by creating high quality assignments, I hope to make formative assessments that will help overall learning.

Develop: I want to teach and model effective self-assessment for students. They need to know how to review their work and make improvements upon it. I want to encode self-assessment into all of my classes as a procedural and instructional aspect of what students do on a daily basis. I want to make grading interactive and meaningful for them. I see the best way to do that is for them to develop the skills in finding their own errors and correcting them. This will take instructional commitment on my part and lots of guided practice. If I want this to work, I must be more consistent this year.

7/25/11 - Accommodations Reflection Activity:
Student disabled by breaking wrist: I would poll students who I thought might be able to handle their workload as well as taking notes for the injured student. In many schools they call these TAs, not adults, but either more advanced, more organized, and more mature students who are able to help the teacher with answering questions with their peers as well as handling their own workload and advocating for the help they need from the teacher or other students.
 * 1) 1- easiest to adapt to:

30 student class that is disruptive and non-cooperative: I would need to slow down a bit on trying to push the curriculum directly and work on classroom community building. I would first ask the students "What would you like to do academically this hour?" and go from there. Other questions would include, "What are some ways that you would like to get help when things seem confusing?" or "How do you like to be helped by peers?" and "How do you most like to give others help when they are asking for help but the teacher does not seem to be able to get around quickly to them?" The key is to reset the class norms and expectations, both from the teacher and of themselves. It is imperative that I not try to cram material down unwilling mental stomachs. It is much easier to create a hunger for the material and have them come to the table and eat freely. A day of community building every few days until things stabilize can go a long way in saving not only the unit but the semester. I have had this problem with my D period (last of the day) and good seating charts don't cut it if they just want to act out. What made a difference was establishing clear meaning for the lesson, not moving too fast for the majority of the students, and making sure that I was patient and allowing them time to think and process. In addition, when I was equitable with my assistance amongst all students, this helped others see that they could also be patient and trust that I would make it to them shortly. More work needed to be done to move to the TA level, but sometimes they helped each other out. Not nearly as much as I would have liked. Confused students seemed to turn quickly into distracted, then disruptive students.
 * 1) 2 Most difficult to adapt to:

Content Advisor meeting 7/20/11
This meeting really focused a lot on the order of content specific material. Some of us had finished most of our lesson plans, others most of our assessments, but everyone had a completed unit calendar and unit overview with standards that we could critique as a group. Personally, Jill's suggestion that I move the introduction of the distance formula to the front of the unit gave me some good food for thought. I am thinking that even though they may have trouble calculating the distance, we can use rulers to start off the unit; at the end of the unit we can double back on the idea and see how it relates to triangles and the Pythagorean Theorem. Not only would this leverage prior knowledge, but reinforce that the most important application of the Pythagorean theorem is to find distances. With all of the Google Maps and Mapquest web engines, I will make sure to leverage this readily available technology to connect it to the mathematics that drives the distance calculations.

Although I have only hand-written 3-1/2 of the 8 lessons in RIO format and have not transcribed and condensed it into the one-page format, I was able to present some of my activity ideas for openers and exit slips. Some specific feedback was to be careful to warn students when having them share their writing with others in a group. I already had a parenthetic note in my LP, but it was good to hear from everyone else that my thinking on this prompt was going in the right direction.

I benefitted from the conversation and suggestions about making the pre-assessment focused on what you would hope that they know for the unit and shying away from directly asking unit content questions. It is so easy to simply ask a simple version of something in the unit, but then reduce the efficacy of the pre-assessment because you fail to get an understanding of the level of mastery in foundational skills. I am planning on modifying the pre-assessment significantly to make sure that it is "pre" and not "post" assessment! : )

At 6:50 we headed to the lab to utilize the time to work individually on our unit plan while Jill made specific comments within our word documents for submittal in our unit plan binder.

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Unit Learning Objectives: 1. Students will be able to use the Pythagorean theorem to find the length of any side of a right triangle. 2. Students must write at least one proof for the Pythagorean theorem using symbols, words, and pictures. 3. Students will be able to use the principles of congruence and similarity to solve real-world problems where geometric relationships are evident. 4. Students will be able to simplify radical expressions and relate radical expressions to right triangles and the Pythagorean Theorem. 5. Students will be able to calculate the distance between two points in a coordinate plan and on different locations of geometric shapes. ======

Content Advisor Meeting 7/11:

(we watched the All-Star Game HomeRun Derby).... uh... not... "I gots jokes"!

1. Reviewed each other's summative plans, made suggestions, comments, corrections. a. my vocab needs to come down a little b. small corrections c. finish rubric (combine some elements regarding writing and clarity/organization)

2. Unit Plan Review a. we agreed that we were up to speed on what was required. (showed Jill the checklist) b. Need to get a rough draft and calendar by 7/20 if corrections are to be meaningful/realistically helpful

3. Jill recommended that we keep the equivalent of a log book for lessons, or do so electronically so that year to year we are not starting from scratch. a. nice summaries of lesson plans b. calendar. I like the "old school" method because it is more usable in the classroom, and also forces organization of thought onto paper.

4. Showed us some summative assessments and classroom activities that her students have completed over the years. Nice work. To give us ideas on how to make units more creative and engaging. a. Jeopardy example b. Relay Race example

5. Ideas we have for unit plans: a. My focus will be the distance formula and the pythagorean theorem unit. I think this is chapter 7 and 8 in the Discovering Geometry textbook that MPS uses.

6. Recap on what will be due on the 20th.... Jill sent out as an email.

7. I worked until 7:45 in the lab on tidying up my SA plan and other corrections before I forgot them, since I had sent Jill my document in .pdf and she was not able to save corrections to a Word file. : )

nite...

Late Work policy comment:

Our discussion made me think of how to promote learning while still keeping the students accountable for work.

Not grading homework will help the late homework crowd because they are not "losing out" by doing it late, only gaining the skill prior to a quiz or exam.

I like the "well in advance" communication policy and I think keeping the guidelines somewhat open for interpretation helps the teacher because some teenagers really seem to like to force you to stick to the policies while they do everything they can to get out of as much work as possible.

the end..

Mark

Session 7- Meeting with content area advisor:

As we entered the room, Jill held up two whiteboards with math questions and used this as a formative assessment. She was modeling what this would look like in a real classroom. Most of the time students would end up waiting in the hall until each individual students had a chance to answer the prompts. Because there were more than one correct answer to the problems, the students had choice.

Jill asked each of us to print off an example of a summative assessment if we did not have one. We all went to the lab and spent 10 minutes getting that prepared.

We then talked about what transpired in class on Monday and what we perceived as the assignment for the Summative Assessment Plan. There was some confusion that was cleared about the use of all 5 modes of question prompts. We talked about each one of our assessments, the format, and the usage. There was good discussion about what is not readily visible from the printed copy such as verbal instructions and how students understand our voice. My final exam could have been clearer and allowed more room.

Jill passed out several assessments. We discussed each one before moving to the next. After seeing several assessments that Jill had prepared, I decided that I will use more multiple choice and matching. Multiple choice is very pertinent since the example of the AP Calc exam was almost all multiple choice and Jill mentioned that every one of those students passed the AP exam. The caveat was that the same teacher taught the pre-requisite class and therefore was able to weed out students who could not handle his very college-like style (flys in the face of what we are taught in the MAT program!!).

We then decided to conduct more peer reviews of our State of the Content paper since none of us had completed the paper.

The big takeaways for me were that I need to include all modes of questioning for that SA plan and that giving multiple choice tests actually can help prepare them for standardized tests and is a perfect example of "assessing to the test", although not to specific test items.

Finis MJ

Research Paper Working Outline: I. A. Introduction 1. Student quote about homework (Cushman quote 2010) 2. Controversy about homework

B.Connector statements 1. Statement about need for better understanding of homework's role 2. Student learning should always be focus

C. Thesis statement presented: 1. Homework and the use of it in the learning process is controversial and requires careful design, possible modification for students with special needs, and deliberate implementation for effective formative //and// summative assessment.

II. Trend #1 - Not using homework/ Best Practice #1- using HW effectively A. Explanation of the trends of not assigning homework 1. dangers using homework improperly 2. traditional tool hard to replace 3. combining new techniques to old practice

B. Cite research from articles 1. Pro homework 2. Anti-homework

3. Concluding thoughts 1. validity of homework 2. must replace with something equal or better

III. Trend #2- Not Grading Homework A. Explanation of trend and reasons behind trend 1. Application in modern classroom 2. What this does for teacher's time - reallocating time 3. Formative only idea

B. Examples in my classroom 1. Issues faced with motivation a. positive b. negative 2. Cited material a .Not a good measure of summative understanding b. for practice and formative assessment c. "Case for and Against" quotes and strategies d. "What is homework for" quotes i. student concerns ii. connection to the extracurricular iii. teacher's concerns and strategies for HW use

3. Concluding thoughts about grading or not grading: 1. traditional viewpoint 2. omission of using for final grade a trend 3. seeing homework differently as practice only 4. tool to extend school day 5. leverage extracurricular connections 6. what does HW point to? communicating purpose key

IV. Trend #3: Homework differentiation A. Best practices 1. Special needs 2. Talented and gifted

B. Examples 1. Simple strategies used in my classroom

2. Cited research: 1. Student interviews 2. Solution dynamics 3. Math specific methods 4. Special needs strategies 5. Talented and gifted strategies

3. Concluding thoughts 1. Difficulties of differentiation 2. HW's benefit in face of difficulties

V. Conclusion A. Restate thesis a. synthesize best practices and trends of homework usage

B. Impact of HW use 1. First to keep it

2. Second how to use it a. Formative is best b. No grading c. Focus is spending time on feedback, not number for grading

3. What must change? a. teachers forced to be creative b. awareness of pitfalls c. avoid shallow understanding levels d. let go of homework as a rule (drill without knowing)

4. Implications of not changing approach to homework a. unable to reach larger class sizes b. unable to meet needs of 21st century problems

5. Thought provoking statements: a. missing opportunity to create lifelong learners b. losing opportunity to engage parents with their children

Session 5 Activities: Discussion on one of the articles posted on the mystritch portal:


 * Article: Writing Boost Learning in Science, Math, and Social Studies**
 * By Peggy Harris**


 * 1. What are the main arguments or points?**

The author, Peggy Harris, supports writing in all classes (including the sciences and math) based on evidence in the teaching field. An improvement in scores on standardized tests is believed to be the result of students gaining a deeper understanding of the topics because they are writing and posing logical arguments to support their understanding.

The author mentions that the process of writing on a regular basis in a math class only strengthens students’ ability to read and write in an English class because the same skills are developed. According to Harris, the reading improvements are especially noticeable with English Language Learners. A key word in this essay is “inquiry”. Inquiry is so much more than “asking a question”; it is the process of formulating questions and presenting them in thought-provoking ways that can lead others to yet more revelatory thoughts and questions.


 * 2. Does s/he support those arguments or points convincingly? Explain.**

The author gives supporting evidence, or claims from teachers at least, that reading skills are improved through the process of writing because students need to process arguments that include causal relationships. The evidence presented for improved reading is mostly anecdotal and not entirely convincing or data driven. Teachers who were cited in the article notably mention that they were given training and materials that helped them implement writing in the classroom effectively. In addition, the contributors noted that trainers were practitioners themselves and gave clear examples of their experiences, what worked/did not work and why. One thing that sticks out for me is that writing “documents the learning” and is “the voice” of the learning process. It can be reviewed, revised, and shaped into clearer and more detailed thoughts. It is flexible and an invaluable tool for students in their quest for knowledge and its application.

The teachers who contributed to the article give the reader some creative ideas for introducing writing in their content areas. In math, for example, the teacher gave the students the framework of the Challenger space shuttle disaster in which they look at data for trends, give opinions based on the data, and wrote from the perspective of those on the decision-making teams who approved the launch.

Social studies topics easily lend themselves to creating assignments. Students write as if they were living in those times and must learn what a person of that time might know or not know, feel or not feel. It is a higher level of thinking to learn about a subject by analyzing what we know today, and what we could not have known in the past. Current knowledge is then not taken for granted. What a sixth-grader knows factually today could have seemed genius 100 years ago, but unless that student understands the complexity and depth of the concepts involved the information is largely un-applicable to the problems of tomorrow. Students’ work was cited as being presented in “real world” (an overused, poorly understood phrase in mathematics) venues such as the newspaper and heralded for its high quality. Infusing the classroom work of novices into arenas with larger audiences (inside or outside the school) brings home the connection of content importance and its usefulness in everyday life.


 * 3.How does the information in this reading support what you will do or do in your classroom? Site some specific examples.**

What teachers seem to be aiming for by using writing in across content areas is for students to gain deeper level of knowing. Conversely, students can demonstrate mastery by expressing what is not known (or perhaps still needs to be discovered). Students are taking information and, through writing, moving it progressively toward conversations in which many facets of the information are woven into a knowledge base. Once this base of knowledge is thoroughly understood, it can be deftly applied to various situations and scenarios.

Teachers in today’s fast-paced curriculum struggle just to reach a basal level of understanding; the reticence to introduce writing in classrooms may, ironically, be the very reason it is so hard to move to higher levels.

I like the article’s mention of writing from different perspectives, especially the exercises with known historical figures or events. There are so many math-based events (not just socio-political) that students can choose from. Education has the odd need to separate mathematical subjects through titles (i.e. trigonometry vs. geometry vs. algebra); this is most noticeable between mathematics and English or history. Mathematics, like any other subject, is woven into the fabric of the human experience. It is historical, social, and physical. It reminds me of when I had a deep realization that the sciences were all just trying to say the same thing, but at different scales: this was not until I took biochemistry in a post-baccalaureate biology track. I hope my students can come to realize the interrelatedness of all studies and therefore develop the skills of anchoring their knowledge to multiple learning environments.

Rote memorization of facts limited to a certain problem, genre, or time period is almost useless unless it can be applied to the world around us. To apply knowledge is to use it to analyze decisions that affect entire cultures and the ideas and technology that drive how people to allocate their time and money.

When I have used instruction time to develop writing activities and student inquiry assignments, the dividends far outweigh the investment. It takes a several hours of modeling and clear direction for students to reach success levels in their writing and feel like they are able to not only explain the information, but to make general statements that are applicable in numerous scenarios. Oral responses are clearer after engaging in a writing assignment and I notice that their confidence level is higher. In a math class, the key quality to have is persistence, and not far behind is the confidence to know that you can reach the right answer if you keep trying.

Students that write to support or refute arguments can more easily ferret out misunderstandings about a concept or skill. I think that is why I need to spend considerable time writing in math class, not in the 5-paragraph essay way, but primarily in the way that forces students to think about what they are doing, why they are doing it, how they can become better at it, and how they can share it to change the world around them.

Content Area Advisor Meeting: She conducted an icebreaker activity which involved arithmetic. MathDan compiled the questions and sent this out in an email. We also talked about which chapters would seems most applicable to the research paper. Most agreed that the chapter on Learning Theory, Curriculum, and Assessment, along with the chapter on Planning would probably apply (after reading one of the chapters this turns out not to be the case for my research topic). She then asked us questions about how we normally go about our daily classroom and how much variety is included on a daily basis. We talked for a while about this and some other teaching strategies that seemed useful. As a final activity, Jill gave us a list of mathematics related websites and we re-located to the computer lab; some sites were self-help for students, others spoke more to teachers and the practice. After about 30 minutes of web-searching, we ended the session.

Thesis statement for research paper: Homework and the use of it in the learning process is controversial and requires careful design, possible modification for students with special needs, and deliberate implementation for effective formative //and// summative assessment.

** Textbook Survey—Mathematics **

As you peruse your content area textbook, please complete the following activities and/or questions. You may place your responses on this page.

1. Write a bibliographical entry for the book using APA format.

Brumbaugh, D. K., & Rock, D. (2006). //Teaching Secondary Mathematics// (3rd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.

2. What are the authors’ backgrounds in education?

Brumbaugh taught at the University of Central Florida. and Rock is the Dean of the College of Education at Columbus State University.
3. Read through the Prefaces. What are 2 things that you learned about the book or author?

I cannot do this assignment without the book...!
4. Looking at the Table of Contents, what are the 3 main sections of the book?

Skills in Teaching Mathematics

1. General Fundamentals 2. Mathematics Education Fundamentals 3. Content and Strategies

5. Which chapter should you definitely read before you begin the unit project?

Chapter 3: Planning

6. What do PTHND stand for?

D - Do the problem or activities before reading further in the text!
7. A general format for a math lesson plan is provided on page 7. How does it compare to the RIO format? (What is similar? What seems missing?)

It has the objectives, how to instruct and guide practice, and provide a summative assessment.

It sort of lumps the instruction, essential questions, and summative assessment into the "Procedures".

8. Of all the chapters in the book, which one interests you the most? Why? Advanced Algebra and Trigonometry. Because, as a former engineer, we used this part of mathematics the most.

9. Of all the chapters in the book, which one will you probably not read during this course? Why?

Calculus. Simply because in the district I teach in, the focus is on the less advanced mathematics and only a few teachers will teach calculus if they are in the right school and with students who have advanced to that level.

10. What is one section in particular that you would like to discuss further with your content advisor? Geometry. Because I may be teaching this, and I need to hone my strategies in this area. This is my weak area.


 * Instructor Recommendations for Reading:**
 * For Research Essay and Unit Planning—Read Parts I and II. Highlight as you read a chapter. Then stop and list your “Top 5 Ideas/Tips” from the chapter. Read only one chapter at a sitting.
 * As you do you the unit plan and summative plan, read the chapters in Part III that are applicable.