My budding love of teaching, stemming from my larger love of math and learning

Saturday, November 20, 2010

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 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.

Thursday, November 18, 2010

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!

Friday, November 12, 2010

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 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:


      • 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


      • 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.

      Saturday, November 6, 2010

      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?

      Thursday, November 4, 2010

      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!

      Sunday, October 31, 2010

      Starting Off a Busy Week Positive

      I have been struggling a lot lately with my decision to be a teacher. At first it was just the thoughts of "Why did I take a $10,000 pay cut?" or "Man it would be wonderful to go out to lunch to day and have a beer." (which I did often as an engineer). But then it turned to really doubting myself and my ability to do this job.

      Three jobs in three years, with no guarantee of having a job next year, starts to play with your mind. The students that make your job even harder, the doing your job during every waken moment...this is the story of my life right now.

      Am I meant to be in this job? Do I really want to be doing this job? And then the idea of teaching Geometry...AAAAAHHHHHAAAAAAAAAHHHHHHHHHH!

      Last week I started the week being pretty miserable. But this week I am going to try to stay a little more positive. I know that the problem students are not being a problem because of me, they are a problem for everyone. I know that everyone is stressed. I know that I am doing a good job, per my observation last week, and that I won't ever be perfect, so why try to be. I still know more than any student in my classroom, and really do they know a bad lesson from a good lesson. I need to make more time for myself, and things will get done. Probably not on the time frame that I have been trying to hold myself to...just a little longer.

      I need to stop letting students control the decisions that I make, and not to let their comments effect my plan going forward. Of course they are going to bitch about the number of homework problems that I give them each night or that a quiz is 50 pts, "That's more like a test!", although quizzes are 20% of their grade and tests are 40%. These students are not my peers, their parents are not people that I socialize with and are not the ones making the decision about my job.

      I know I can survive, but I am not sure that I want to. Do I really want to teach?

      Friday, October 29, 2010

      New Way of Grading?

      Ok, I think I am going to try something new with grading. Not sure that I should be doing this at the end of the quarter, but I don't see what the difference is really.

      Here's the idea: Students earn their grades, right? So why have I been taking points "off" on test/quizzes? Why haven't I been giving students the points that they earned on each problem. In the past I have be subtracting 1, 2, 3, etc. points when they make a mistake, but this time around I am going to give them 5, 4, 3, etc points that they earned with the work they have done. Isn't this essentially the same thing?

      I have been reading a few blogs lately that focus on Standard Based Grading (SBG) (Miss Calculate, Pt of Inflection, f(t), amongst a few others), and it is not what happens in my school, but I really believe that it is the way to go, and I am hoping that I will be in this position next year so this summer I could work on implementing SBG in a way into my classroom (right now I am just trying to get the content out to the students in a cohesive, understandable way).

      Ok, so back to my new way of grading. I am going to try this:
      • 0. Has not demonstrated any skill or understanding (i.e wrote nothing down)
      • 1. Hasn't completed much work on the problem (tried to start the problem, but really there is no conceptual understanding of the problem)
      • 2. Has completed a little more work on the problem but, still lacking the conceptual understanding of the problem, and is making mechanical errors (i.e. computation errors)
      • 3. More understanding of the concept, but using wrong thing to solve the problem (i.e, used Alt. Int. angles when they should have used Corres. angles, or said that corresponding angles are supplementary when they are really congruent).
      • 4. Has demonstrated mastery of the skill, but is making mechanical errors ( i.e. Set up problem correctly but did 3y = 108, y =39, or forgetting to carry a negative through.
      • 5. THe problem is done correctly, correct set up, correct explanation, no mechanical errors, all formulas shown correctly.
      Students can earn half points. An example of this would be the student did the problem correctly but did not write any formulas down (I am HUGE on writing the formula every new problem you do).

      I am sure I will get some fights from the students on this because of not really understanding (the same students that complain a quiz is worth 50pts, saying that is like a quiz, but quizzes are worth 20% of their grade and tests are worth 40%, also the same students that would complain if I put $1M in front of them). But I am going on the fact that students EARN grades, and I shouldn't be taking points away from them.

      I ask you, readers (if there are any out there): Is it ok to change to this way? I really think I am not doing anything differently, just adding points instead of subtracting. Opinions?

      Tuesday, October 19, 2010

      Trying to be more hands on...

      So earlier this month I attended the regional NCTM conference in Denver. I am very lucky that a regional conference ended up being so close to me, but not so lucky in that I ended up having to pay for it myself and that I was the only person to attend from my district. But I pushed to be able to go and I am soooooo glad that I did. There were so many great things that I am little by little trying to implement in my classroom. I saw a great response by a reader of MissCalcul8; this reader told her that "this year you only have to get half way to perfection". It is my new mantra!!!!

      Ok so on to the idea that I am going to try tomorrow. I went to a great hands-on workshop by Gary Kubina (I tried to google him but not much came up, so no link), it was called 'Hands-On/Minds-On Geometry". One of the activities that he did was called 'Planes & Lines'. You were given two lines (straws) and two planes (index cards) and you needed to model certain situations, such as, 'a line intersects a plane at a point', 'two parallel planes', 'two planes intersect in a line', etc. It was AWESOME, why didn't I think of this when I was desperately trying to get my students to understand a 2-D picture was a 3-D situation. So I am going to try it tomorrow as we start to talk about Parallel Lines & Transversals.

      Here is how I am going to implement it (my students sit at tables of two):
      Each table will have 1 ziplock bag with 4 index card, with holes punched in two locations (2 per student) and 4 straws (2 per student).
      Using the items in the zip-lock each student will have to model the following situations, they may not have to use all four items for each situation:
      • A line intersects a plane at a point
      • two lines are skew lines
      • two planes are parallel
      • a line is parallel to a plane
      • two planes are parallel
      • two planes intersect in a line
      • two lines intersect in a point
      • two lines intersection a plane in two distinct points, the two lines are skew
      I think there are some classes that are going to love this. Then I think there will be some kids who wouldn't be happy if there were a Million dollars in the bag too.

      Here's hoping it goes well.

      Monday, October 18, 2010

      Struggling with In Class Examples

      I am struggling with in class examples. I am not sure what to do. Here's my problem: Algebra examples are easy for the kids to copy because it is usually an equation/expression or a short prompt. Geometry examples tend to be much longer and my students are not quick with the quill if you know what I mean. So what do I do? I have been getting phone calls from parents (ok just one parent) saying that I have not gone over concepts prior to assigning HW, which I know is not the case and typically spread a lesson over two days to make sure that we spend time on examples.
      I would love to be able to give each student a copy of the ppt slides (I do this so that I don't have to write every example, and project it directly to my white board. I am toying with the idea of giving each student a half of sheet of paper with the prompts. But in this time of budget crunches...can I really use all that paper.
      I don't do the book problems because I have found that students don't pay attention or process the information as well because the answers are right there, so I use the additional examples from the Teacher's addition.

      What do I do?

      Friday, October 8, 2010

      NCTM, Denver 2010

      WOW!! 2 fun filled days of math. I learned so much. Hoping I can find the time to get everything up here, but since I have posted since the end of August, maybe winter break will be a good time.

      Wednesday, August 25, 2010


      I survived! I survived the first day of school in my third new school. I have no more to write because I am brain dead and I still need to figure out what I am going to do tomorrow. But yes I am alive.

      Wednesday, August 18, 2010

      Not As Painful

      The last three days we have been curriculum mapping in our district; at the start I thought it would be really painful. I was mostly scared of inputing the State Standards. I get dizzy looking at the standards. Up to this year, CO standards were confusing and wordy.

      Well things weren't as painful as I thought it would be.

      Since math is kind of a textbook driven subject (more on this later), most of what I needed to input into the ATLAS curriculum map was straight from my textbook. First I made a unit for each of the 13 chapters. Second, I used the title of each lesson within each chapter for my content. Then I used the objectives for each lesson as my skills (bold action verb of course). And lastly (the part that was the least painful of the day, but I thought would be the worse) was importing the state standards.

      Why was this not painful you ask? Because my textbook company ROCKS!!! Glencoe/McGraw-Hill is AWESOME. They have matched the Colorado state standards for Mathematics (the new ones), which by the way have not even been loaded on the CDE website (go on, I dare you to find them, because if you do you should be in the FBI), to the content in the book. It was so easy to follow the document and choose the appropriate standards in the ATLAS program.

      Now a note on the textbook driven statement: I am a teacher and I want to be the best teacher I can be. So this year because I am new to teaching Geometry, I am going to follow the book. I am hoping to revise objectives as I go along, as well as write essential questions and supporting questions.


      Tuesday, August 17, 2010

      I Actually Won Something...

      I never win anything that is by chance! My name never gets drawn out of the hat, I don't win the scratch tickets, I am never the 1 millionth shopper.

      This morning our superintendent started off the day by pulling names out of hats for things that she had picked up at a teacher store earlier last week. There were some great things and it was exciting at first seeing all the great things, then I remembered...I don't win things.

      Well wasn't I surprised when she said my name...I was SHOCKED actually. I was just starting to say to my neighbor, "my name NEVER gets pulled out of hats".

      I was able to pick up the game Spot It!, I ran down the aisle just like on the 'Price is Right' (actually our art teacher was humming the theme song in the row behind me), picked up my prize, and went back to my seat to read the directions. Then my head started to what a great game and I could totally adapt this to content...if I had time.

      So when I get time I am going to try to make a content specific game on Spot It! I am not really sure how this is going to happen yet. I am probably going to try to set it up in MS Excel. But I will definitely be sure to post it here when I do.

      Monday, August 16, 2010

      Just like onions: “The more you peel them back, the more you want to cry.”

      I make it a point to not really talk politics. I am not a poli sci major, I don't teach gov't and I get my source of political news from Joe, Mika, and Willy (and Luke Russert when I get lucky...just a little crush there ;)) on Morning Joe. I have other things to focus on in my daily life (i.e. Essential Questions, learning targets, engaging classroom activities). But this is one political measure that I will talk about and I will campaign with all my might AGAINST!

      If you live in Colorado and are a registered voter (if not GO HERE and register), I urge you to please, please please VOTE NO on Amendments 60, 61 and Proposition 101.

      I am not going to explain each ballot measure here. I will turn you to the Coloradans for Responsible Reform and their website 'Don't Hurt Colorado'. Each measure is explained here, and an explanation of why it would be bad for Colorado is included.

      I was aware of these measures prior to this morning, but I didn't realize the impact that they would have on our district if passed. Looking at the cash flow and budget graphs I was scared out of my mind. We have a balanced budget, we have worked on a balanced budget (no thanks to the state changing the fiscal year in 1993), and if these measures are dismissed, we will continue to work on a balanced budget, was the message I got this morning from our superintendent. If these measures pass, we will not have a balanced budget, and there is a possibility that we will have to close our doors because there will be NO money to operate.

      Supports of these measures are put it nicely. They run shady campaigns and use the method of "we'll keep quiet and hope voters know nothing about a initiative until they read it on the ballot; ensure that the ballot question characterizes complicated initiatives as little more than tax cuts." The politicians that support these measures are being backed by individuals that will profit from privatized education, which is where education will go if public schools have to close their doors. With 38% (and as high as 89% in some districts) of children in Colorado public schools qualifying for free/reduced lunches, can you imagine what will happen to those children that can't afford to go to school. Might end up looking a little like our health care system.

      If these pass they will not only hurt schools, but also small business owners and eventually all members of a community. For example: Prop 101 will actually decrease funding to road services, including snow plowing. Um we live in COLORADO snows here...A LOT. You live on a county road...touch luck, you won't be getting out when that 12 inch storm comes, which means you can't get to work. You think that is going to save you $$$.

      There is a lot of information out there on these ballot measures, I urge you to PLEASE be educated when you vote on Nov 2, 2010. Please don't get caught up in the smoke and mirrors of the supports of these measure, because that is just what it is smoke and mirrors. In anything that I have read tonight, I have seen no solutions to the problems, all I have seen is "this will help the state", well HOW will is help the state. There are no hard numbers. If you read new articles, websites, blogs against these measures, numbers and $$ projections are given and it is SCARY!!!!

      If you are reading this and you are a registered voter in another state, PLEASE make sure that you are educated on your ballot issues this fall, because I am sure that there are other states out there too that are facing similar issues.

      This isn't written very eloquently, but it was written passionately.

      Friday, August 13, 2010

      Completely OVERWHELMED!!!

      I don't even know where to start. With going back to school full time starting Monday, my to do list just keeps getting longer and longer and longer, and what do I decided to do...write this post.

      To Do (no particular order because I don't know where to start:
      1) Finish setting up room (post bell schedules, make tardy sign sheets,
      2) Finish writing syllabus (3 all slightly different), write supply lists for students
      3) Get ready for 3 days of curriculum mapping (objectives, essential questions, etc.)
      4) Read Student/Staff Handbook
      5) Write/Prepare materials for first couple lessons
      6)Decide on how my 3 classes will be set up
      7)Plan first two days of school...i.e. intros, class explanations, handing out books, etc.
      8)Print class rosters with column for book numbers

      And lots and lots and lots more stuff that I can't even think of right now.

      Wednesday, August 11, 2010

      Inception...Not the Movie, but What We Do As Teachers

      When I saw this movie, I wasn't really expecting to go to it that night. It is not usually the type of movie that I would spend $9.50 for a ticket and $9.00 (well half of this) for a Hot Date combo (never actually shared with a HOT DATE).

      The night I went was the night before I left for a 3-day Colorado River trip. My mind was filled with: Did I remember all my gear? Am I going to make it through the rapids rowing on my own for the first time (I was super super super nervous)? Is it going to rain, because I didn't bring my tent? And, Do I have enough adult beverages to sustain me for 3-days, on the river, through the desert, with the sun beating down on me?

      So, within 30 minutes of pulling into my friends place for the night, we were planning on walking out the door to go to the movies. Like I said, not usually what I would have spent money on...I would have picked 'Despicable Me'. But my friend M. Payne loves movies, and 'Inception' was right up his alley.

      Walking out of the movie theater the only thing I was thinking was "Wow, who was the 'genius' that combined 'The Matrix', 'Vanilla Sky', and 'Ocean's Eleven' into 1 film and thought it would be good." I think it goes without saying it didn't instantly become my favorite movie and and I didn't give another thought to it, didn't applying any of it to my live, and get my sights on my 3-day river trip.

      BUT then I read Tom D's post on 'Inception', and again he has BLOWN ME AWAY. I would NEVER had linked this movie to what I inspire to doing with my teaching. I am not even going to try to repeat or throw my spin on what his thoughts are because I am still processing it all. He has given me more to think about going into this school year. What we do as teachers is INCEPTION! If you are teacher, and plenty of my friends out there are, please read Tom's post on Inception. I can only hope that one day I can be settled in my curriculum and can start thinking about teaching the way that he does. Thanks again Mr. D!

      Monday, August 9, 2010

      Where do I buy the fireworks?

      So as I sit here and try to write out some lesson plans I am wondering to myself, WHY BOTHER? Everything you need to know is right in the book: Definitions to vocab words, examples, guided practice problems, even the problems that you should assign from homework.

      So why am I spending so much time on lessons? Because I have decided that the book is boring. It is how you and I were taught math. Who wants to sit there and be lectured. Even asking the kids questions can get boring. Now I understand that every lesson can have the "bangs and whistles" but a little excitement...and not just for the kids. I get bored too!! And I LOVE LOVE LOVE math.

      I use a lesson template with 5 sections from Conscious Classroom Management by Rick Smith:
      Intro: Whet the students appetites
      Direct Instruction: Direct the learning/Facilitate, without necessarily lecturing
      Guided Practice: Provide opportunities for students to work with new material/ideas Independent Practice: Encourage student autonomy
      Closure: Emphasize key Points

      I try to bring in parts from the 5-E Instruction Model (A frame-work for Inquiry Based Instruction):
      Engage: Gain Attention
      Explore: Facilitate students' thinking
      Explain: Help students to create meaning
      Elaborate: Apply and extend learning
      Evaluate: assess student learning/gain feedback

      The 5-E Model is more appropriate for science learning, but why shouldn't it be used in the math classroom. I mean, math can be inquiry based, right? So I use a combination of both...or at least I try.

      Where I get caught is with the Intro/Engage. When I taught science it was really easy to have a cool Intro/Engage or it is sometimes called a Hook. I get stalled out when trying to think about initial engagement, and then I am not focused on the rest of the lesson. Which is usually too bad, because I spend so much time on trying to think about at great hook, and then I don't put what needs to be put into the independent practice/elaborate. And that's when I should be really good because I am the engineer, I have used most of this math in a real-world situation.

      So my goal for this year: Write a great total lesson plan, and not worry about the "Fireworks" hook; I am going to focus on fun in other parts of the lesson. I think that is all for now.

      Tuesday, August 3, 2010

      I Swear I am NOT a Horder

      Or at least I don't think I am. My mother might beg to differ after moving many many boxes just over a month ago.

      Now let me explain why I "might" be a horder: I still have all my grad school books, binders (I graduated from grad school in Dec 2003), as well as many many teaching resources I have collected over the last 2 years. I have this need to have resources around. I think it comes from not having the confidence that I won't actually be able to recall it when necessary. But anything that is in those grad school books is now readily available online. There really isn't any need to have the binders full of notes and assignments. Except...I think that one day I will create AMAZING lesson plans from those assignments...if I am ever in a job long enough that I could revise my curriculum to bring in more real-world applications.

      I started thinking about this as I moved about 10 boxes into my new classroom this afternoon. I wondered...what's in all these binders (None of these binders actually being grad school binders).

      So MAYBE I am a Level 1 Horder. But I did spend sometime yesterday condensing the binders from my 7th grade lessons into one 2-inch binder. I only kept the things that I did not have electronically. I also pulled out three binders from my first year of teaching as well as my teaching program portfolio. I am almost positive that have most of this stuff electronically as well. So my plan tomorrow is to head to school with my external hard drive in tow and clean out those binders too, keeping only those things that I DO NOT have electronically (checking the hard drive prior to throwing anything out), and hoping that somewhere in the building there is a scanner that I can easily scan that stuff too. So I am working towards whittling down.

      So does this make me a horder? I don't know. Hopefully by this time next week, I can feel differently.

      Friday, July 30, 2010

      I have...Who has...

      One of my favorite games for the classroom is "I have...Who has..." It is an entire class game and it keeps the kids attention because they never know who has the answer. I used it a lot in World History by making my own for the Egypt, Rome, and China units. It was a lot of work to make them. I wanted to get to a point where I would make them in math, but never got around to it and put in on my "list of things to do this summer". Well that list hasn't really gotten any smaller this summer.

      But while perusing math blogs this afternoon I found several versions of the game on Mathwire. And I remembered my "list of things to do"...why recreate the wheel. I love it when teachers share things and don't expect any payment. Teachers are poor...we are here for the betterment of the students, and why recreate the wheel?

      I have gotten some awesome games from this site. I usually get pretty overwhelmed because there is SOOOO much on this site, so I tried to only go to it when I am looking for something specific. But I stumbled upon it today while reading a new blog Let's Play Math.

      Thursday, July 29, 2010


      If there was one thing I learned last year it was "set you expectations" not just in how you expect your classroom to operate but also in what you expect the students' work to look like. I expected my 7th graders to have some sort of knowledge of what work should look like before they turned it in. You know what I am talking about: Name clearly written, assignment written on the page, problems labeled with the appropriate problem number, space between each problem. OH BOY WAS I WRONG!

      I received work that didn't have the assignment written on the paper, which would be O.K. if students didn't turn it in late. I ended up having to find the problem in the book and then match it to the assignment given, which would have worked if the student wrote the problem, but that usually didn't happen either (they just wrote an answer...not any work shown either). Always a lot more work for me.

      What else: usually not stapled, fringy garbage from sprial note books (pet peeve!), no name, 15 problems done on 10 lines of college-ruled paper, no numbers or letters of problems, answer not clear, pen (green, purple, florescent pink), scribbled out work in both pen and pencil, and the list could go on and on and on.

      So this year I am not taking any chances. Yes my students will be in High School, but I can't assume anything. So I am including in my syllabus a Criteria-for-Credit. This is a suggestion in a book that I got from a Spence Rogers conference I attended my first year teaching, and I am finally starting to consult the book. The book is Teaching for Excellence, I think there is a newer version out.

      Criteria-for-Credit are standards that must be met in order for the work to be accepted as done. These standards are the SAME for all students (with maybe some differentiation for some lower level students). Student work not meeting the criteria-for-credit must be adjusted to meet the criteria before it will be accepted.

      So here is what will be posted on the wall of my classroom:

      In order for my work to be accepted by Ms. S it must meet the following standards:
      • Neat (clean, unwrinkled paper with smooth edges, you can use one-sided recycled paper)
      • Properly Labeled (Name, Date, Class Period, Assignment in upper right-hand corner of the paper)
      • Problems Copied
      • All Steps Shown
      • Work Down
      • Answers Labeled Appropriately
      • Blanks Left Between Problems
      • Answers Boxed or Circled
      • Done in Pencil (Erase, Do Not Scribble out)
      • Follow Assignment Directions
      What am I missing?????
      I would like my students to ID appropriate examples of Criteria-for-Credit, so I am thinking about trying to make a game out of it for one of the first days of school. Something funny and but making it be totally obvious what the answer is. I think I am going to have a white board in my classroom, so I am hoping to make something we can use the clickers with.

      Saturday, July 24, 2010

      I see myself as a student striving for great knowledge and a better understanding of both my particular role in life and life in general. -- Kay Toliver

      Audrey F. is a great teacher. She works as a kindergarten & mentor teacher at a dual language elementary school. The district that Audrey works in always has a great professional development line up for the first couple in-service days of the school year. (I had the privileged of attending my first year teaching because that was the district I worked in, and if I weren’t already going to be in school this year, I would probably sneak into the workshops this year).

      Last fall I received a phone call from Audrey after she had attended these beginning of the year workshops. She said “ER, I just had the best workshop. Kay Toliver is AMAZING. I am not even a math teacher and I want to teach math now because I had this workshop. I am sending you a copy of this DVD and you HAVE to watch it”.

      And she did. Then for the 4 months every time I talked with Audrey she would say, “ER have you watched those DVDs yet? No, why not?!?! They will change your life!” She would post on my Facebook page, “ER, have you watched those DVDs?”

      Well, finally on xmas break while sitting in the Buffalo, NY airport, I finally popped in the DVD. WOW…why had a waited sooooooo long to watch these videos? Let me tell you, the way that Kay Toliver teaches is how I have envisioned that I would teach since I decided that I was going to be BORN AGAIN. Ms. Toliver describes her style of teaching as “teaching and learning through listening, speaking and writing.” Isn’t this how all teaching should be?

      I realized that I wasn’t teaching this way. I was feeling so much pressure to get through content that I wasn’t able to full embrace what Kay was doing. I wasn’t teaching problem solving, I was teaching content and I was teaching content in a way that I was shoving it down their throats…NOT the type of teacher that I want to be.

      The past couple of days I have been reading whatever I can find about Ms. Toliver. There isn’t much out there that is FREE. Although she was once an inner city classroom teacher, I believe that she now makes her living in professional development for teachers. Here is a link to one of her videos about Triangles in Architecture.

      One the best statements that I have read is the one that I used at the beginning of this post. Ms. Toliver has also written, “I believe that every student can succeed in math, even if they have never been successful before.” And I guess this is my mantra for this upcoming school year. And I am going to keep telling myself that, I am going to tell colleagues that, and I am going to tell parents that if I have a chance.

      From the videos that I have (about 16), I am going to write up lesson plans for my classes. Each video is only about 10-12 minutes long, but I think that I can write up a pretty decent lesson from what is shown. I am going to implement most of them in my Pre-Algebra class. It is the class that I have a little more freedom in. This class will consist of those students that have never truly been successful in math before, but it is going to be my goal this year to help them achieve this success. I am really excited about the flexibility that I am going to have in this class.

      My geometry classes I don’t have as much freedom in. These are mostly college bound kids, and the amount of content that I have to get through is A LOT!! But I am hoping to implement little bits into those classes, and hopefully after a few years (will cross my fingers every day that I will be at this job for a second year) that those classes too will evolve, or you could say be born again.

      Thursday, July 22, 2010

      End of the Year Student Feedback

      This past year I taught 7th grade, wow-o-wow. Were we like that in 7th grade? Honestly though, I have to say I loved it. I had a great team that I was a part of and learned so much from them all. It was a challenging year, not only because I taught 7th graders math (which I am more than qualified to do), but also because I taught 7th graders World History…yes you can laugh now. But I had an amazing AP World History Teacher in high school (thanks Mr. Carver!), a great mentor at 7th grade WH, and a life-long-learning passion, so I was able to pull it together.

      One of my favorite blogs to consult with over the year was I Want to Teach Forever by Tom Derosa. The end of the year Tom posted “student feedback questions”. Because my life was sooooooo crazy the last month of school (52+ job applications, 2500 miles driven, 8 job interviews, 1 PLACE exam, only 1 job offer), I didn’t get to give these questions to my students until the last couple days of school (after I was offered a job and accepted).

      I wish I had given them to my students in early May, because many of their answers would have helped me out during my interviews. They are still great to reflect back on, to make changes in my teaching for this year and to use if I am ever in an interviewing situation again…I hope this doesn’t happen for a few years.

      This is modified from one that Tom posted. Half of the questions were for the students to rate themselves (not included), the other half to give feedback on my teaching. I am going to share some of those answers with you. I have included positive and negative. Everything can be used for improvement.

      If you found out your friend/family member was going to be in Ms. S’s class next year, what would you tell him/her?
      …don’t be a jerk to Ms. S b/c she is pretty awesome
      …she’s really nice but don’t piss her off
      …she has her day
      …she will push you to get better grades
      …stay on task
      …a little tiny bit strict about showing your work

      What did Ms. S do well this year? What should she keep the same when planning for her classes next year?
      …not giving too many assignments from book – boring!
      …have a sense of humor
      …when you do something wrong she lets us give it another try
      …taught in fun ways
      …learning easier steps to hard problems

      What did Ms. S NOT do well this year? What should she change when planning her classes for next year?
      …yelled a lot
      …more group projects would have been more fun
      …she should have told us to do all the problems
      …when she was stressed she would take her anger out on us, but I know she was just trying to get through the year and help us out
      …pushing me to turn in my homework
      …she should have more games
      …nothing she was GREAT!

      What 3 words would you use to describe Ms. S?
      …funny, cool
      …awesome, fun, nice
      …organized teaching, not organized desk (more than 3 words, but true)
      …mysterious, funny, joyful
      …humorous, sensitive, awesome
      …snazzy, smart, fantabulous
      …fun, crazy, helpful
      …laughable, smart, creative

      What is one thing you will remember most about this class?
      …your laugh and smile
      …the fun
      …always do you homework or life sucks
      …having Ms. S tell me I did well
      …she cared about the NCAA basketball tourney.
      …always show your work
      …when you move the decimal over two places it looks like a butt cheek
      …how she makes me laugh

      Anything else you would like to tell me?
      ...thank you 4 teaching me
      …you are an awesome teacher and I will miss you
      …you were wonderful
      …I learned a lot, thanks for everything
      …probably one of my favorite teachers (even though you were a little pissy sometimes)
      …you will do amazing at your next job
      …very nice, considerate teacher
      …have fun
      …keep going the way your going
      …way to go!