Saturday, November 20, 2010
Thursday, November 18, 2010
- 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")
- 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)
Friday, November 12, 2010
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.
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.
- 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
Thursday, November 4, 2010
Sunday, October 31, 2010
Friday, October 29, 2010
- 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.
Tuesday, October 19, 2010
- 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
Monday, October 18, 2010
Friday, October 8, 2010
Wednesday, August 25, 2010
Wednesday, August 18, 2010
Tuesday, August 17, 2010
Monday, August 16, 2010
Friday, August 13, 2010
Wednesday, August 11, 2010
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
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
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
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
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
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
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?
…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
…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
…keep going the way your going
…way to go!