Angle Pair Practice

So this week I used a worksheet from Ms. Cookie @ Math Teacher Mambo on Angle Relationships. Although we finished Chapter 3 about 2 weeks ago, I realized that my students needed continuous practice on the topic. They think that everything is congruent, even though consecutive angles are an acute and an obtuse angle (in most instances)...I mean REALLY, do they even look the SAME!!!!! Use your common sense!

When I stumbled upon this worksheet I knew it would be perfect. I gave the students the worksheet a week prior to the quiz and told them that I wanted them to try to fill it out on their own, which I think most of them did. Then early last week we review the worksheet together and we went over each figure. I put the worksheet underneath the document camera and zoomed in on each box. I asked the students to give me the relationship and explain why. I thought it went pretty well. I did call on different students each time, and did accept the answer "I didn't do that one", I just said "OK, if you had, what would the relationship be". Putting my students on the spot? Sure...they should have done their homework (Ugh...another post all together).

The students were told that they would have a quiz on this worksheet. There were 25 correct responses, each correct response would earn them 1 pt. However, to keep those couple students from circling every answer, I also told them that they would loose 1 pt for each incorrect response. So in reality, they could get a negative score, which I would just give them a 0 if that happened...hoping that this wouldn't really happen. I mean if you were not positive of the answer, just leave it blank...it wouldn't hurt you. I felt this would be a great assessment tool.

82 students took the quiz (a few students out sick)...1 student...ONE!!!!! got the full 25 pts. Needless to say I was a little shocked. Eighteen students got above a 20...I was happy about that. I knew I would have a lot in the teen range. There were a lot of 17s. But here comes the shocking part...there were 17 students that got a big fat 0! 17!!!!!!!!!! WOW! And there were quite a few 1s and 2s as well.

I really don't want to grade things again. Sometimes I do not believe in redos, although that is a premise of SBG. I have decided that I will not give them class time to do redo this. I am going to put a sign up on the wall: 7:30, 1st lunch (Junior Senior study hall), 2nd lunch (freshman, sophomore study hall), 4:20pm. They need to sign up for a time, if they do not show up, then they loose the chance to retake it. I am sick of waiting for kids that do not show up. But I also feels like this puts the responsibility back on the student. Even though I am they one that will be grading them...AGAIN!

We'll see who shows up and takes the opportunity to redo the quiz.

PS This post was written while riding the Amtrak home...AMAZING WiFi on a the train.

Encouraging Words

Although I am technically a long term sub, my principal is treating me as a first year teacher, which I look at as promising for next year (YAY!). So about a month ago, I had my first observation of the school year. Leading up to the observation I was pretty nervous. I had been questioning my ability to do my job, my wanting to do my job and the idea that others thought I could do my job. (See previous post) I had my pre-observation with my principal, she assured me that the feedback that I would receive was not meant to be critical, and I assured her that I understood that and I was actually looking forward to her being in my classroom, because I wanted the corrective criticism.

I did not plan and elaborate lesson plan. I am a true believe that you should be observed on what's happening in your classroom everyday, not something exciting that might happen every once in a while. The night prior to the observation, I went through my example problems several times trying to anticipate questions from students. The group of students that would be in my classroom during the observation has several higher level thinkers in the classroom; a few that questions EVERYTHING. Which is not a bad thing, but the the questions sometimes catch me off guard. So I just wanted to make sure that I was ready.

And ready I was. I felt great during the class, I felt great after the class, but still really nervous about what she would have to say. Then I got the observation form from her through email. It was good, I mean I think it is good at the time. Here were my strengths from my principal (black) and my thoughts (red):

• Knowledge of subject matter (This I knew...I'm an engineer, so I know the material, I think I need to do a better job of funneling the information to a level that is easier for the kids.
• High expectations for student behavior, respect between teacher and students is apparent (I needed to hear this. I had been struggling with the idea that the students respected me, or were they just respecting me that day because the principal was sitting in my room?)
• Preparation for successful classes (I work really hard making easy to understand ppts, making handouts for the students with the figures for the lesson, and making sure I know the problem by heart so that I don't look unprepared by looking at my notes, so this was great to be recognized on it)
• Curriculum mapping use and completion (um, ok...I guess this means that I stated the targets before the lesson, but I wish I did a better job of questioning the students about the targets at the end of class)
• Use of technology-overhead prepared materials (I use a ppt everyday. It makes it easier on me so that I don't have to draw the figures every example problem)
• Willingness to assist students outside of class (I do offer my time to the students, but not many take me up on it. I also will not force students to come in. Choices, choices, choices, maybe that stems from me starting my teaching career at a "school of choice")
• Confidence in presentation and responding to student questions (I made myself be confident that day...I repeated the line from 'Cool Runnings' in my head, "Well, let me tell you what I see. I see pride! I see power! I see a bad-ass mother who don't take no crap off of nobody")

Areas for Growth or Concern:

• Generalized questioning, towards more specified questioning -- Hold greater accountability for student learning (This is something that I struggle with every time I write a lesson. I want to ask better questions, lead them down more detailed paths, but right now I am so concentrated on funneling the content. I feel like this is something that gets better the 2 or 3 or even 4th year that you teach the content. I am so hoping that I am able to have that opportunity)
• Don't be so hard on yourself! You'll burn out of this profession if this is always an emotional high. Hang in there and keep relying on your mentors and administrators (I have started to say "NO", more to myself than anyone else. I need to find a balance, and right now there is no balance)

So all in all, I felt pretty good about what my principal wrote in the form. I was having more confidence in my teaching ability and just my overall wanting to be here.

Then the post-observation conference came...and things got even BETTER!!!!!!!!!!! My principal told me that she was very impressed by my teaching, that I am a great teacher. Do I have room for improvement, yah, everyone does. She acknowledge the difficulties I was having with some of the students do not go unshared. She also acknowledge my frustrations on other topics as well. She assured me that she felt confidence in her decision to bring me on board. And truthful...I do work with great people (mostly).

I needed this boost of confidence. I know that I am making a difference in some students education. The students that I am not reaching, may be in that group that no one can reach. I do laugh with some kids, I have had kids tell me that they actually understand it now (more my Pre-Algebra kids), and I know that some do like me (one in particular always brings me artsy things to hangup). I guess I do like my job, and I know more now that I am doing a good job.

So I am off on Thanksgiving Break in 40minutes. I am walking out this door for 10 WHOLE DAYS!!!!! I am off to New England for some family and friends. I wish I could say that no work will be done over this time, but alas I have grading and lesson planning that I need to do. But at least I am not walking down these hallways. Adios!

12 Weeks (more of less) of Diary Mapping

The district I work for is having each teach curriculum map 1 class that they teach using Atlas Rubicon. A curriculum map is something that I have wanted in each of the three schools I have been in (in the past 3 years), so I am actually pretty on board with the requirements, although I have hesitations because I don't know for sure that I will be at this school next year. But that is a whole other post, so I will just say...I am trying to stay positive.

I easily mapped my Geometry curriculum because math is pretty driven by the text book. Yes, you can elaborate, but because it is the first time ever teaching Geometry, I am sticking to the book and adding things as I go along (like Billy Bob's Road Kill Cafe...which I am going to try to get in a post about soon). So, although I have been told that my map is too book driven (duh, it is a book based class), I mapped it using the objectives straight from Glencoe Geometry textbook, and I am trying to add essential questions and supporting questions as I move along. I am struggling with this though, because I am focusing trying to plan the content in a manner that is easy for my kids to understand.

We have an inservice about once a month. Last month I got out of it because I attended NCTM in Denver; this month...no such luck, I had to go. So because my map was done, I focused on Diary Mappying, which one of the requirements of the map. I am not sure how other teachers are diarying (word??), but I think mine has evolved form being detailed, to just asking questions of myself, that I hope to be able to go back and look at once I have finished the entire course.

So below are my diary entires over the first 12 weeks of school:

Chapter 1 - Tools of Geometry:

Supporting Questions are being added throughout the unit as I am seeing what the bigger picture is. I have added a few supporting questions, but they are definitely being changed as I move through. Using some of the "Higher Order Thinking Skills" Problem for Supporting Questions.

Points, Lines, Planes (1.1) (This lesson took 3 days, but I think it was because of problems with visualizing a 3-D situation, see below)

• Hard lesson to start on. Lots and Lots of vocab words. Do not really want students to address vocab words on their own; trying to set norms for how students should be taking notes on vocab words and notations as part of their journal. I feel like I am not going fast enough, and afraid that I will be questioned on my lack of rigor in the classroom.
• Also I am finding it hard to have warm-up problems as part of the beginning of class. Maybe I should start putting a time limit and letting students know when that limit ends.
• Students had a hard time visualizing the 3-D image of intersecting planes. For the next class I made a card-board representation of the intersecting planes. It definitely helped most student see what was happening.
• Some of the more advanced students struggled with the idea that there were only two planes defined, they understand that there are an infinite number of planes, but they are not understanding that only 2 are defined. I have told them that if there are 3 or more that it will be clear and that I will not try to trick them.
• Exercises: #54 students struggled with the directions of "Satisfying an equation", so got tripped up on the entire problem; #51 d is not necessary; #50 students did not know what a vanishing point was; #52, many students did not using a problem solving technique, they just assumed that they did not have enough info to solve the problem.
• Spiral Review of Algebra Skills: Radicals, Solving systems of equations, Graphing points to create geometric figures, metric conversions

Linear Measure (1.2)

• Students are struggling with the fact the definitions are to for their use to be prepared for the next lesson, they are not HW, I will not be collecting them.
• Needed to clarify to students that lines and segments will/can have the same name, with the different designation symbol over it.
• Quickly running through examples 1 & 2, w/ the assumption that students at this level should be able to use and read a ruler to measure a line segment.
• Students are lazy about writing the "betweenness equation", needed to remind them of practicing notations with simple problems, so that we encounter more difficult problems we are clear about the notations. For example: writing it using subtraction.
• Spiral Review of Algebra Skills: Solving Inequalities, Evaluating Expressions

Distance & Midpoints (1.3)

• When I introduced the distance formula through theory first, it was a disaster!
  • Stepped back to teach it again, first talking about the Pythagorean Theorem and finding the distance by drawing a right triangle between the points. Then talking about how a and b in the theorem could be replaced with the name of the segment. Then talking about how we would find a and b without drawing a picture (i.e. subtracting the values of our coordinates). Talking about a general form of the equation we end up with. And then ending with the Supporting Questions: "How do are the Pythagorean Theorem and the distance formula related?"
• Students are fighting the need to write formulas on every problem. Trying to stress to students that there are so many more formulas in Geometry than in Algebra, and many more packed into 1 lesson. Also trying to explain to them the need to do it because of proofs, and that is the make up of Geometry.
• Spiral Review of Algebra Skills: Solving Equations

Angle Measure (1.4)

• Short quick lesson. 1 day on content, spent another day on (short day Tuesday) on constructions: Copying of angles and Bisecting of Angles.
• No need to do 2 examples on naming vertices and all the angles with that vertex.
• Stress the need to use the notation for congruent angles and measures for congruent angles are equal.
• Starting to get away from the solving of the variable together. Continuing to set up the problem for them (progress check = having a student give me the steps), but focusing my talking time on the concept at hand, not the algebra 1 content of solving for 1 variable.
• Gave students hand-out with figures because of the complicated nature of the figures, saved on class down time.
• Use the example from "Personal Tutor" for example 3. I felt as though the one in the original ppt was too wordy for the concept to be addressed, and the REAL-World situation was not relatable.
• Questions #41 & 39 were difficult for the students to visualized. Stressed the need to sketch the figure. WOrked through 1 or the other with the class, but NOT both. They are essentially the same problem except for the algebraic expressions given for angle measures.
  • May want to suggest that students distribute the 2 in the expression representing the measure of angle ABE, so they are working with 2s + 11. Some students are not doubling the angle, rather assuming the angle is doubled because the original expression is 2(s + 11)
• Questions 30-35: Have students copy the figure from the book (gave them a blown up copy) using a straight edge and compass only to practice copying an angle and bisecting. The figure is not drawn accurately, so when doing this, the right angle symbol should be IGNORED!!!!
• Gave the students a copying the angle sheet, as well as step by step instructions on copying and bisecting an angle.
• Spiral Review of Algebra Skills: Measurement Conversion, Solving Equations

MID CHAPTER QUIZ -- Gave students the distance formula and midpoint formula.

Angle Relationships (1.5)

• Day 1 (1/2 class): Gave students two tables, "Relationships do to Angle Positioning" & "Relationships due to Angle Measures". THis is how I addressed vocabulary (Adjacent, Linear Pairs, Vertical, Complementary, & Supplementary Angles). Used language from text book, but put it in less wordy terms. Stressed the importance of the notation formulas for Complementary & Supplementarty relationships, and the NEED to use them.

Looks like maybe I didn't finish diarying this chapter.

Chapter 2- Logic & Reason:

2.1-2.4

• I didn't have the kids write enough related conditionals.
• Students struggled with inductive vs. deductive. Need to do more practice with inductive/deductive statements together.
• I need to explain better the purpose of a Venn Diagram as related to Logic. i.e. the conjunction is the intersection of a circle, a disjunction is the union of the two sets (circles)
• Proofs: Why aren't these being taught? I know students struggle with them, but it is so important in their thinking process moving forward. The higher level students want to know where certain theorems come from, which they would understand from the proof process. Should probably teach as a fill in the blank process.

Chapter 3

3.1

• need more practice on IDing angle relationships without parallel lines, understanding that there is no congruency or supplementary relationships unless the lines are parallel
• I like the paper folding activity to make the angle relationships
• do not do the making a cube again...students thought it was stupid and didn't see the point. Maybe bring in several cube boxes, maybe try to make a pyramid, and a pentagon prism for examples on skewed lines and parallel planes. Have them do a walk around activity and ID skew and parallel via hands on.

3.2- Angles and Parallel Lines

• Like paper folding activity to create parallel lines and a transversals. I think that the really could see the angle pair relationships.
• I need to do more practice on looking at relations created by parallel lines and those created by non-parallel lines. Doing now as an activity in the next chapter, will be quizzed over them. Using the Angle-Pair Relationship worksheet that I got from Math Teacher Mambo (under resources). Need to change the sheet to say that it is consecutive interior angles rather than same-side interior angles. Hoping to get the original word document from the author.

3.3 - Slope of Lines

• WOW...amazed at how many students struggle with slope.
• Need more practice on the slope relationship between parallel lines and perpendicular lines
• Wondering if worksheets would be better for students then bookwork. i.e. getting students to write down problems. What about having them graph every problem AND do it algebraically.
• What about a slope only quiz?

3.3 - Equations of Lines

• students only want to use slope-intercept form and fight the idea of using point-slope, although student forget what to do with the "b" once they find it and regularly put the point back in to y=mx+b and leave b and m as the variables.
• Would more practice be all they need? Why aren't they better with this skill?

3.5 - Proving Lines Parallel

• Some struggles with this chapter because we haven't really talked about proofs. Tried doing informal proofs, but students fight the requirement of writing reasons. Wondering if doing proofs in Chapter 2 would remedy some of this.
• I think because we didn't do enough related conditional statements, the students do not recognize that we are working with converses of the theorems.

3.6 - Perpendicular Distance

• students struggled because of the long problems. They are lazy and don't want to do all the steps. They want to find a short cut, but one does not exist. I wish they would trust me on the fact that there is not a short cut. DO they not trust me because of the informal proof process I am making them do? If we were doing formal proofs would I allow them to not do the informal proof process on every problem? Is the informal proof process to repetitive for every problem? Should I really make them show the steps of Def. of Congruency and substitution every time? OR would it be ok if they just stated the theorems they used at the end of the problems?

4.1 - Classifying Triangles

• Do I need to have a lecture on this section. Could I give the kids skeleton notes for classifying triangles by angles & classifying triangles by angles within in figures, and have the level of discourse in the class be raised a little? Creating more student-student discussions? Maybe do 1 problem where you have to find the missing value problem?

4.2 - Angles of Triangles

• Would love to have students discover the "Triangle Angle-Sum Th." on their own through a flow-chart graphic organizer from me. Do I have time? The flow chart could lead into a flow proof...two birds with one stone?
• The above statement could lead into the "Exterior Angle Th." discovery too.
• students are confusing Ext Ang Th (m<1>

4.3 - Congruent Triangles

• Need to be more clear to students that when writing congruent statements for segments that congruent angles need to match up (i.e. Segment AB is congruent to Segment DE, not Segment ED).

SSS, SAS, AAS, ASA, & SSA, AAA (4.4 & 4.5)

• Billy Bob's Road Kill Cafe - First attempt was ok, but I need to revamp it to see if it can go smoother.

Over Teaching?

What does this mean?

As a sit on my couch on a Saturday night and write my lesson plans for the week, a comment made to me during PTCs keeps running through my head.

I had a parent say to me that her daughter (who, mind you, is 15 years old) made a comment that I was over teaching. I was shocked to say the least, but my response back was this, "I teach to the mid-level student, you daughter is slightly above the mid-level student. I follow the curriculum in the book, and I do examples that support that curriculum".

I usually discuss content definitions/theorems and then do 3-5 examples depending on the content. I make the students think about the next step in each problem and then tell me what should be done. I want it to be more hands on, but I have been told to pick up the pace, so I am doing the best I can with the time restraints given to me.

Now, I ask you...what is over teaching?

Week in Review

Well this wasn't as busy as a week as I thought it was going to be...but I am writing this before it is officially over, so we'll see. And I am only getting to write this in the middle of the day because all my Geometry classes are taking an end of the chapter test.

I started off this week writing a blog about staying positive, which I am having a really hard time doing. For several reasons:

a) some of my students, and some of their parents

b) confidence in my ability to be teaching this subject

c) my desire to be wanting to teach this subject

d) the demands of my job not related to the classroom

As I started the week telling myself I was going to be positive. I was able to put a few things into perspective and I think it helped. Even coworkers have made comments on the change in my attitude. I know that October is a really bad time of the year for me. I let the decrease in day light really effect me, and I don't start to make a change until it is too late. I upped the amount of vitamin D that I take and I tried to recognize when I got down.

As this week went on I realized that I am doing ok. Of course, there is always room for improvement, and I know that. And I keep going back to advice that Miss Calculate got from one of her readers, Emily..."You want to be the best teacher that you can be, and that won't happen if you spread yourself too thin. Remind yourself that you only need to get half way to perfection this year, the rest can happen next year."

My connections with students are improving. There is a more carefree attitude in my classroom. There is more laughter. I had a boyfriend in grad school that went to Africa for a time a few weeks. He came back with a piece of cloth that the women there wear. On it was written in the native language (I can't remember which country he went to, so I can't remember the official language) "Your laughter puts me at ease". And even though that relationship is long over and we have both moved on with our lives, on completely different paths, I still have that piece of cloth in the bottom of a tupperware bin, not because it was from him, but because it was really cool! And I still think about it occasionally. This being a perfect time to talk about it. When my students are giggling, when I can giggle...there is so much ease in my classroom.

We started parent-teacher conferences last night. I was really nervous, for several reasons.

a) I didn't want to take to the parents that I have talked to several times via phone or email. I mean what else do I have to say?

b) I didn't want to talk to a mother of a boy that I recently suggested that he move back to Algebra, even though the boy als0 felt he could be more successful if he went back (this student took Algebra as an 8th grader, and was a freshman in Geometry)

c) I was worried that there were going to be conversations with parents about my need to differentiate, in both directions

d) I was afraid I was going to hear that students really disliked my class.

At the end of the night here's how I felt.

1) I enjoyed the way PTCs were set up at our school. Rather than teachers being in their rooms by themselves, secluded from the heros that would sweep in if you were getting chewed out by a teacher, we were all in the commons together. All the round tables of the school were put in there and teachers were only separated by 4 feet or so. Which was awesome. I could watch the interactions happening at the other tables. And I felt safe if an of those "crazy" parents decided to try to corner me.

2) I saw those parents that I have communicated with via phone or email walking around...they didn't come see me. Which is FINE with me! But I was prepared to say several things to them, to defend my teaching style, methods, and philosophies. To let them know that I am well aware of their students copying answers out of the back of the book for homework, and that was probably why they were doing well on quizzes/tests. I was also prepared to invite them to my classroom to join class any day if they had a question about what was actually happening in my classroom.

3)I did speak to the mother of the boy that went back to Algebra...she was totally on board!

4)I did have a few discussion that centered around "what are you doing for my gifted child". One father said to me "Well, I'm an engineer, and I understand this stuff, so why aren't you doing this. And isn't geometry about tiling?" My response, "Oh, I'm and engineer too, undergrad and masters..." Him "Here in Colorado?" Me "No, I went to Syracuse UNiversity. And yes there is Geometry involved in tiling, but this is a proofs based Geometry class, so that is what we are focusing on." And he went on and on about needing to see the book. I said "Go-go gadget ear muffs!"

Another mother suggested that I allow her student to have a journal inclass. "Wouldn't it be great if she could journal about what is going on? I know that you are teaching to the low students in that class...juniors and seniors...she is getting bored." Me "Well I believe it is important for all students to be part of the discussions. Geometry is very unlike any other math, because it is based on proves and the students aren't quite sure on the process yet. Even if she thinks she gets it, there is always another theorem or postulate to learn. I am happy to challenge her more on the homework, but she needs to learn to be attentive in class." So I am sticking to my guns. I am not going to make more work for myself.

5) I had some great discussions with parents about how the kids like my class. I was surprised...but happy. And several students that I didn't expect it from.

All in all the first night of conferences went well, I can only hope that tonight is as smooth.

Lastly, I am feeling really good about my decision to grade on a 5 point scale. I think it is going to make my grading a little easier. And this way I don't need to try to figure out point value prior to the test, I just say "All problems worth 5 pts".

All in all, it has been one of the better weeks. I hope I am not jinxing myself!