Carrie+and+Marakina

__Homework/Journal__

__//**August 23, 2011**//__ 1) According to the article, U.S. teachers may have more culturally approved ways for teaching math, but Japanese teachers have more detailed and widely shared methods for effective teaching. Are these necessarily exclusive or is there some way to combine the two methods? 2) After reading the entire article, I wonder if the authors are suggesting we copy the Japanese Instruction guide or come up with our own.

__//**August 30, 2011**//__ __Two things I’m looking forward to__. First of all, I love the idea of refining and perfecting a lesson. I think taking the time to review and improve this lesson will make the process seem less daunting and will become easier to do with future lessons. Second, I’m looking forward to collaboration with other teachers to find new things to do with my classes, and in my lesson planning to improving my teaching.
 * __Lesson Study Process__**

__Two things I’m concerned about__. First, I’m worried about taking time off teaching to watch the lesson being presented. I’m not sure how many times we need to give the students the lesson, but I am concerned about taking time away from my students and my teaching. Second, I’m worried about personality conflicts among the teachers. I believe we all have strong ideas about the best way to work with our students and the best way to plan our lessons, and I don’t want this process to be stunted by arguing about the best way to plan and execute the lesson.

I haven’t seen or used any tasks last week. However, I have only had about a dozen students for about 10 minutes on Thursday. My 7th grade students came to their orientation day and rotated through their classes, only staying in each class for 10 minutes. My students start back at school full time tomorrow morning, August 29th.
 * __Tasks used in the classroom__**

__//**September 6, 2011**//__ There are a few things that I have noticed that make a good group. One is making sure there is a definite leader. This person is usually in charge of keeping everyone on topic, moving the subject along, watching the time, and settling disputes. A second thing that is needed to keep a group on task is minimizing “outside” chatter. It’s very tempting to talk about non-work subjects, but if everyone is willing to commit to maintaining the topic at hand, then the meetings will be more productive. Third, in a perfect world, all decisions would be unanimous. Using a “majority rules” method to make decisions, may leave some people frustrated, hurt or angry. If this happens, the group dynamic is thrown off, and can make it hard to work with each other. Finally, the kids need to come first.

__//**September 13, 2011**//__ This article seems to nicely sum up a majority of the problems plaguing our society. The list of the problems the students gave sound like things my students would say about current and past teachers. I do believe as a whole, most teachers have gotten better about knowing their subjects and therefore are more passionate about them. However the remainder of the observations/complaints may still be valid. I would like to know how we can increase our expectations, make the subject real, make the subject challenging and not teach to the test when our jobs are based on how well our students perform on the state standards tests.

I don’t believe that the system is meant to turn our children into “a passive mass”. But I do believe that this system is set up for the teach to the test method. We need to find a way to combine the methods that our system currently uses and the methods that will enable our students to learn how to think for themselves, how do to more than regurgitate information for the test and then forget it. How can we get our students interested in the subjects we teach when their lives are so involved in the “now”, in the “stuff”, and in the current time, not the past or the future. Or at least not the future unless they get a kick in the pants, like “Brian” at the end of the article.

__//**September 27, 2011**//__ I feel as though we need to be somewhere in between the two extremes. I see the value of teaching "school algebra", as this leads to problem solving, and I don't believe our students can understand or appreciate "college algebra" without starting with the basics. I also agree that there are several different variations in the way we look at variables and the confusion they introduce, not only for the students, but for the teachers as well, can cause several problems. We need to find a way to make the different variable types more common and more understandable for our students. For some, I believe they think the role of algebra is just something they need to learn in order to move on. I believe there are others who see algebra as the gateway or the building blocks for other math classes they will take in the future. Some see it as an insurmountable, complex system that they need to struggle to understand, while others see it as a series of patterns or puzzles they need to solve. I don't know if there is an easy way to reconcile the differences. If we want to change the way our students view algebra, we need to change the way we teach it. However, this is much more complicated than it sounds. Trying to find new and different ways of showing the kids something they don't know, or something they do know in a different light is hard and requires a lot of research and time on the part of the teacher. We need to make the decision, individually, about what is most important for our students, and what we need to do about it.
 * __**How does the role of algebra as you see it compare to Usiskin's ideas?**__
 * __**What do you think your students think the role of algebra is?**__
 * __**How do you reconcile the differences?**__

**__October 4, 2011__** I tend to use gathering information, probing, generating discussion, and exploring mathematical meanings and relationships. There was a lot of “why”, “what do you think”, “who can back that up”, “can you restate that in your own words”. I try to get my students to discuss topics among each other, not just hand out right answers, or try to get the students to come up with solutions among themselves, instead of just saying yes or no. I have noticed this method works better in my honors classes than in my regular classes. They are more willing to talk to each other, to discuss why their thoughts and theories are correct or incorrect. In my regular classes, my students are more unwilling (or unable?) to have these conversations. I’m still trying to decide how to make the connection from “right/wrong” answers to “let’s discuss this and figure it out”. They are even more willing to come up to the board and work problems in front of the class, my regular students, in general, don’t want to volunteer or work in front of the class. I really think this method could help my regular students solidify their mathematical understanding, or even make it easier for them to know how to do the problems, even if they don’t understand the why’s of how it works.
 * __Questions:__**

Readings: So far I have found something helpful out of every article or chapter we have read. I do appreciate how the reading has been broken down into manageable sections, instead of larger chunks. Discussions: The class discussions do seem to go rather deep into some subjects and therefore take a lot longer than they should. At times I feel as if we are just going around and around the same subjects. On the other hand, there are times when the extra discussion brings around better understanding on our part, which makes us better mathematicians, and hopefully better teachers. Group Work: Again, this feels like we’re going around and around in circles. I feel as though the last week we spent the whole time discussing things that could have been decided on in the first 10 minutes. Because we spent the whole time “discussing” what our lesson should be, who will give it, where our lesson will fit into our unit, and finally what other lessons should be in the unit, I we lost time discussing things I feel are more important. I feel that we should have spent the last class adjusting the lesson that is going to be taught, or writing objectives for the unit.
 * __The course so far__:**

I have often felt the same way Cathy did, I want a community of learners in my room, and I believe this requires students to engage in discussions, and I also didn’t want to put my kids on the spot, but asking for volunteers always results in the same few students doing the talking. I would like to have the same kind of discussion Cathy had with my students, but I don’t know if we have the relationship that would help them understand that I really want to know what they are feeling. However I don’t know if the students have the understanding and willingness to have small group discussions on the correct topics. I feel as though they will spend the time talking about other things, or not talking at all. I wish I knew the best ways to bring about effective small group discussions with a bunch of middle school students.
 * __Chapter 7__**

__**October 11, 2011**__

__What I considered as I was writing the lesson plan__: I knew it was a review lesson before a unit quiz, and I wanted to be sure my students were comfortable with the rules of exponents. I wanted to have several different ways of allowing my students to show off their knowledge and work the problems, so the information would be accessible to all my students.

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__How the lesson went__: The first time I taught the lesson it didn’t go very well. I felt rushed the whole time, trying to fit in several different types of work: individual, partners, and class. I felt as though there wasn’t enough time for each different section. So I changed it up the next few times. I reduced it to two different types of activities, and in one case (6th period), I only used one activity, the partner work with whiteboards. =====

// __**Lesson Plan**__ // Content Objective: Students will be able to recognize and apply exponent rules for specific problems. Language Objective: Students will be able to verbalize directions and adequately explain exponent rules in their own words.

Starter (5 min): 1) What does “expanded form” mean? 2) Name all the exponent rules we have learned.

Part 1 (5 mins): As a class, but students do work on their own paper. From section 1 of the Walkaway Review, work problems 8, 10, 4, 6, and 2. First write in expanded form, then simplify. Students are to work individually, then write their answers on their whiteboards. We don’t move on until the entire class has the correct expansion and simplification.

Part 2 (10 mins): Pair work. From section 2 of the Walkaway Review, work problems 13, 11, 19, 15, and 17. For 5 minutes student A will tell student B how to work the problem and what to write down, then we switch and student B will give student A directions. I will circle the room during this time and help students with their directions. be clear and precise in your language and directions.
 * Possible help: “why this way?” “how do you reason out or remember rule?”
 * Directions for partner work: Writer – write down what talker is saying, not what talker means. Talker –

Part 3 (10 mins): Individual work. Pass out worksheets, students start at #26 and work backwards. They need to circle the problems they have the most difficulty with, and we will cover some of those questions during the last 10 minutes of class. I will not go over a question if no work is shown on the students worksheet.

Part 4 (10 mins): Wrap-up. We will go over some of the students individual questions. I will not give answers, but instead we will talk about how to decide which rule we need to use and what processes we will need to use to simplify the problems. During this point, I will pass out the Exit Tickets.

Exit Ticket/Homework (5 mins): Exit Ticket: “Which rule do you struggle the most with and why do you struggle with it?” Homework: finish worksheet. Bring most challenging questions for tomorrow. We will have time to cover 2 or 3 before the Walkaway.

// __**Modified Lesson Plan**__ // Content Objective: Students will be able to recognize and apply exponent rules for specific problems. Language Objective: Students will be able to verbalize directions and adequately explain exponent rules in their own words.

Starter (5 min): 1) What does “expanded form” mean? 2) Name all the exponent rules we have learned.

**//__Choose one or two of the following parts, based on the needs of each individual class.__//**

Part 1: As a class, but students do work on their own paper. From section 1 of the Walkaway Review, work problems 8, 10, 4, 6, and 2. First write in expanded form, then simplify. Students are to work individually, then write their answers on their whiteboards. We don’t move on until the entire class has the correct expansion and simplification.

Part 2: Pair work. From section 2 of the Walkaway Review, work problems 13, 11, 19, 15, and 17. For 5 minutes student A will tell student B how to work the problem and what to write down, then we switch and student B will give student A directions. I will circle the room during this time and help students with their directions. and precise in your language and directions.
 * Possible help: “why this way?” “how do you reason out or remember rule?”
 * Directions for partner work: Writer – write down what talker is saying, not what talker means. Talker – be clear

Part 3: Individual work. Pass out worksheets, students start at #26 and work backwards. They need to circle the problems they have the most difficulty with, and we will cover some of those questions during the last 10 minutes of class. I will not go over a question if no work is shown on the students worksheet.

Part 4: Wrap-up. We will go over some of the students individual questions. I will not give answers, but instead we will talk about how to decide which rule we need to use and what processes we will need to use to simplify the problems. During this point, I will pass out the Exit Tickets.

Exit Ticket/Homework (5 mins): Exit Ticket: “Which rule do you struggle the most with and why do you struggle with it?” Homework: finish worksheet. Bring most challenging questions for tomorrow. We will have time to cover 2 or 3 before the Walkaway.

**__October 18, 2011__** Comparing the habits of mind and the 8 mathematical practices, they seem very similar. The habits of mind seem like the 8 mathematical practices all wrapped up in each other. The different habits are mindsets that will help our students work to obtain the 8 mathematical practices in their school work. I really don’t see any major differences, nothing really stands out as a difference, however I believe the students are inclined to different habits of mind and may not be able to think easily in other manners. I do believe every student can use the 8 mathematical practices.

My own habits of mind tend to lean towards pattern sniffing, describing, tinkering, and guessing.

My students are so varied that I believe they all have different habits of mind. I don’t see as much tinkering or conjecting as the others, but overall I see many different habits from my students.

In my teaching, I try to get my students to connect what we are doing right now and what we have done previously that might be similar and how we can use our past information to work with our current problems. I try to get the students to describe what they are doing and why, not just randomly throwing out work. I try to encourage my students to see things in different ways, trying to visualize what is going on. I try to make sure my students understand the rules behind the mathematical shortcuts, before they use the shortcuts.

**__October 25, 2011__** Response to feedback: __Is a unit quiz same as a unit test__? This is a review for a Benchmark. A Benchmark is what Jordan School District (JSD) has decided to call their end of unit tests. __How many quizzes/tests are there per year__? JSD has created 7 Benchmarks for 8th Grade Math. As a math department, we have decided to give one or two Walkaways (10 question quizzes) to be given between each Benchmark. __How many reviews are there__? Usually there is one review for each Benchmark, but no review for a Walkaway. __How many other things are there that might be taking the time away from the instruction__? I work in a middle school, so there are several things taking time away from instruction: picture day, assemblies, field trips, school counseling groups, family vacations, etc. This is one of the reasons we (the other 8th grade teacher and I) give reviews before a Benchmark test. Because our students have so much going on in their lives, we feel it levels the playing field for our students who have missed classes and those who have a harder time processing information. __Why is it important that the students know names of rules__? For this question, I wasn't so much concerned with the names of the rules as I was with the situations when we use exponent rules and what those rules entail. __Were they (6th period) able to stay engaged and on task in one long section like that__? Amazingly they did stay on task and were working well. This is the smallest class I have (only 22 students), and the students were more than willing to continue working and were enjoying working individually or in small groups with their whiteboards. If they had started showing signs of boredom, frustration, etc. I would have changed the method of instruction and moved on to something else. The problems were from a review worksheet the other 8th grade teacher and I created. I chose the problems we worked on based on the type exponent rule that was used to try to judge my students comfort levels with the different types of work shown. __What format for lesson plan do you usually use__? I normally use the format that I used for this lesson plan. I will bring another lesson on Tuesday. I have inserted a copy of the lesson plan below.

__**Lesson Plan for October 24, 2011**__ __Content Objective__: Students will explore concepts of very large or very small numbers. They will use scientific notation to calculate how sizes, distances, and earthquake magnitudes change under new conditions.

__Language Objective__: Students will explain (verbally or in written form) why we use scientific notation to describe large numbers.

__Starter__ (5 min): 1) Name one good thing that happened over fall break. Perform the operations: 2) (2.6 x 104) + (5.7 x 104) 3) (7.3 x 10-3) – (3.7 x 10-3)

__Part 1 (5-10 minutes)__: As a class, discuss problem 3 from the worksheet “Scientific Word Problems”. 1) What information do we have? 2) What does this information need? 3) How can we use that we have and what we need to come up with the actual size of the dust mite? 4) How would we write this number in standard form? 5) What are the benefits and drawbacks of scientific notation? Of standard form?
 * The image of a dust mite from a scanning electron microscope is 1.5 x 102millimeters wide. The image is 5 x 102 times life size. How many millimeters wide is the dust mite?
 * Possible questions to ask:

__Part 2 (5-10 minutes)__: In pairs, discuss problem 1 from the worksheet “Scientific Word Problems”. 1) Would a diagram/picture help? 2) What do we know and how can we make use of this information? 3) What operations should we use and why? 4) Which number form is easier to work with, standard form or scientific notation?
 * You are supposed to go to Mars. The earth is 9.3 x 107 miles from the sun. Mars is 8.3 x 1011 miles from the sun. How far is it to Mars?
 * Possible questions to suggest:

After question 1 has been discussed, move on to question 2. 1) What do we know and how can we make use of this information? 2) What operations should we use and why?
 * You can travel 5.88 x 1012 miles in one light year. How many years will it take you to get to Mars?
 * Possible questions to suggest:

__Part 3 (Remainder of class)__: Individually complete the remanding 5 problems. Any questions not completed in class are homework and are due tomorrow.

__**November 1, 2011**__

Unit Goal: Students will be able to (1) understand congruence in terms of rigid motions and (2) prove geometric theorems
Unit Objectives: A. Students will create convincing mathematical and non-mathematical arguments.
 * Lesson 3: Warm-ups for Proof
 * CCSS: G-CO.9. Prove theorems about lines and angles
 * Simple knowledge, application
 * One class period

B. Students will be able to practice writing proofs using congruent triangles.
 * Lesson 4: Writing Proofs.
 * CCSS: G-CO.10. Prove theorems about triangles.
 * Discover a relationship, algorithmic skill
 * 2 class periods

C. Students will learn some techniques for coming up with mathematical proofs of geometric facts
 * Lesson 5: Analysis and Proof, Part 1 and Lesson 6: Analysis and Proof, Part 2
 * Comprehension, communication, application
 * 3-4 class periods

D. Students will combine experimentation and proof to help refine their understanding of congruent triangles.
 * Lesson 7: Investigations and Demonstrations
 * Discover a relationship, algorithmic skill
 * 1-2 class periods

E. Students will learn about the relationship that is congruence and notation for describing congruent figures.
 * Lesson 1: The Congruence Relationship
 * CCSS: G-CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
 * Construct-a- concept, simple knowledge
 * 1 class period

F. Students will be able to devise several testes for triangle congruence.
 * Lesson 2: The Triangle Congruence
 * CCSS: G-CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
 * Application, algorithmic skill
 * 2-3 class periods

G. Students will explore possible congruence tests for quadrilaterals and other figures.
 * Lesson 8: Congruence in Quadrilaterals and Beyond
 * CCSS: G-CO.11. Prove theorems about parallelograms.
 * Appreciation and application
 * 2-3 class periods

Each lesson contains the objective given to the student
 * The lesson number from the text book
 * The Common Core state Standards associated with the given lesson
 * The skills the students will develop during the lesson
 * The number of class periods it should take to complete the given lesson (Note: 1 class period is 45 minutes long)

__**November 8, 2011**__ Unit Goals: Students will use informal arguments to establish facts about triangles, about the angles within the triangle, and the angle-angle criterion for similarity of triangles. Students will prove theorems about triangles. Unit Objectives: A. Students will use inductive reasoning to make and test conjectures B. They will analyze conditional statements and write the converse, inverse, and contrapositive of conditional statements.They will explore how conditional and biconditional statements are used to state definitions. C. Students will use deductive reasoning and logic to develop simple arguments. D.Students will learn what can and cannot be assumed from a diagram. E. Students will use properties of equality, algebra, and the laws of logic to prove basic theorems about congruence and angle relationships.
 * Lesson 2.1: Use Inductive Reasoning
 * Application, Discover a relationship, Simple knowledge
 * 1 class period
 * Lesson 2.2: Analyze Conditional Statements.
 * Communication, Discover a relationship
 * 2 class periods
 * Lesson 2.3: Apply Deductive Reasoning,
 * Application, Communication, Comprehension
 * 2 class periods
 * Lesson 2.4: Use Postulates and Diagrams
 * Algorithmic skill, Communication, Discover a relationship, Simple knowledge
 * 2 class periods
 * Lessons 2.5-7: Reason Using Properties from Algebra /Prove Statements about Segments and Angles/Prove Angle Pair Relationships
 * Algorithmic skill, Application, Comprehension, Discover a relationship
 * 6-7 class periods

F. Students will use proportions to identify similar polygons and find the scale factor between two polygons.
 * Lesson 6.2: Use Proportions to Solve Geometry Problems
 * Algorithmic skill, Application
 * 1 class period

G. They use a scale factor to find corresponding lengths in similar polygons.
 * Lesson 6.3: Use Similar Polygons
 * Application, Construct a concept, Discover a relationship
 * 2-3 class periods

H. They use the AA Similarity Postulate, the SSS Similarity Theorem, or the SAS Similarity Theorem to prove two triangles are similar. NOTE: 1 class period is 45 minutes long.
 * Lesson 6.4/5: Prove Triangles Similar by AA/Prove Triangles similar by SSS and SAS.
 * Application, Appreciation, Communication, Comprehension
 * 3-4 class periods

Lesson Plan: