At the end of 2nd quarter, just before Christmas break, I gave my Geometry students a test that consisted of problems that are more indicative of what I believe common core aligned test questions will look like. Everything that I've read and looked at about CCSS aligned questions suggests that they will involve more reading comprehension and that students will need to be able to tie together algebraic and geometric concepts fluently. As I had somewhat expected, my students results on the test were less than stellar. As a result, I spent a good portion of Christmas break thinking of how to stretch my students' thinking and yet not feel like I was expecting too much out of them. I especially found it difficult to figure out how to work on their reading skills.
Somewhere through the course of my thinking, I developed the idea of giving my students worksheets to complete that would lead them through the notes I would typically have given in class. My job became less of a lecturer and more that of a facilitator. At the beginning of the chapter, the students were given a list of notes and corresponding assignments. Periodic quizzes were also built into the schedule. For example, the students work through 2 sets of notes and their corresponding homework. Answer keys are available so students can check their work. After this is complete, students take a quiz over that material. Two lessons and two homework assignments later, students take another quiz over that new material.
In this way, students are given the opportunity to work at a rate that is more fitting for them. While the chapter outline did include suggested dates of completion for each assignment, quiz, etc, the students have the freedom to work independently at their own pace. I have the students grouped by ability and have found that the small groups tend to work at about the same pace. The students were also told the last day that the Chapter test can be taken. They were also instructed that they are to work at a pace that ensures they can complete at least 3 chapters by the end of the quarter.
This is somewhat of an experiment. I have never operated my class in this manner. I have found that the students tend to have even more reading troubles than I have expected. Simple phrases like "draw a circle centered at A that passes through point P" confuse them. I have also found that while the students tout being much better at algebra than geometry, their algebra skills are much less proficient than they should be. I have heard the comment "You expect me to remember algebra!?" a couple of times. Students do struggle with this much freedom. This is something that I will probably limit if I am to repeat this type of teaching in the future.
I'll keep you posted on how this all turns out.
Monday, January 14, 2013
Tuesday, January 1, 2013
Triangle Centers
I am in the process of working through a series of lessons on triangle centers. So far, I've made it through the perpendicular and angle bisector theorems, as well as perpendicular and angle bisectors of triangles. I am posting what I have accomplished here in an effort to get input on whether these seem to be too difficult. Are my expectations too high? My students are average level sophomores. I am wavering on including more basic skill level types of questions along with the problems currently on the worksheet.
I have considered updating parts of it by incorporating some sort of technology investigation using either TI-84s or 92s, but would have to incorporate some sort of training on how to use the Cabri environment before looking at triangle centers. I think this would be especially useful in portions of the investigation into angle bisectors of a triangle.
I thank you in advance for any help or advice.
Perpendicular Bisector Theorem Investigation
Angle Bisector Theorem Investigation
Perpendicular Bisectors of a Triangle Investigation
Angle Bisectors of a Triangle Investigation
I have considered updating parts of it by incorporating some sort of technology investigation using either TI-84s or 92s, but would have to incorporate some sort of training on how to use the Cabri environment before looking at triangle centers. I think this would be especially useful in portions of the investigation into angle bisectors of a triangle.
I thank you in advance for any help or advice.
Perpendicular Bisector Theorem Investigation
Angle Bisector Theorem Investigation
Perpendicular Bisectors of a Triangle Investigation
Angle Bisectors of a Triangle Investigation
Monday, December 31, 2012
The Silent Struggle
There is a common misconception that teaching is an easy profession. People make ignorant comments about how teachers only work 9 months of the year. This somehow gives people the "right" to imply that teaching is not to be taken as a serious career choice. We are called at all hours of the day, both at work and at home. We're told that we are the problem when a child struggles; the (subject specific) vocabulary we use is above their level of understanding. We're told by parents that if we could only give their child more one-on-one time that it would help (but no one seems to have a suggestion on how to do this with a classroom full of students).
But, I digress. That is not the problem, albeit well known, to that I want to address today.
As 2012 winds to an end, I look back on a year of triumphs and tribulations. My oldest child graduated from high school, but quickly decided that her time was best spent traveling the countryside, jumping from one house to another. I never knew where she was or when she might call. I kept paying for her cell phone with the hopes that she would call, even though she would rarely answer my calls. Thankfully, she is back home now, with plans to attend the local community college beginning in January. Our middle child finished his senior year of football, both a happy and sad occasion following years of practices and games. The youngest had a successful first year in 4H, began playing drums in the school band, and picked up piano lessons.
So where is this headed? I am the type of person that makes to-do lists and am quick to try to delete items from said list. As teachers we know that this list is simply a cycle of making lesson plans, teaching, grading homework/tests/quizzes, answering emails, making phone calls; the list goes on and on. Clearly there are not enough hours in the school day to complete all of these tasks. Some of it must be brought home. And therein lies my problem. I find it difficult to enjoy life when I see so much work just waiting to be completed. For example, today is New Year's Eve and my husband and I have been planning a viewing of Les Miserables for the evening. But, seeing the upcoming days of school on Thursday and Friday, I find that I am more drawn to work on my lesson plans for those days. I feel the stress building up. I look back at this past year and see multiple instances of sitting through school concerts or games, but thinking not of the joyfulness around me. Rather, I am thinking of the most efficient way to accomplish the loads of work waiting for me at home. Some days, like today, I find it difficult to even think of leaving the house.
I don't know how to get past it. How do I balance the demands of my job and the life with my family? About the middle of November I decided that my life was of more importance to me. While I did pack up papers and bring them home in the evening, I rarely worked on them. I spent time watching TV with my kids, working on homemade Christmas presents, and enjoying some time alone. While this did help me feel less guilty as a parent, it also meant that I had LOADS more work to accomplish while at school. And somehow this all worked out. Time just seemed to become available.
So, I write this post not to inform you of my personal struggles, but to let others teachers (be they new or veteran) know that life should come first. Don't let your job consume your life. Enjoy every minute you have. Live in each moment, don't just be a participant. I noticed this change most at my daughter's Christmas program. I watched the faces of each child: the quirky ones, the let-me-sing-in-my-loudest-voice ones, the kids with the squeaky clarinets, and I truly saw what I had been missing all along.
So tonight the work will wait. I will grab a BOX of tissues and the hand of my loved one. I will sit in a quiet theater, most likely crying, and enjoy the moment that I have with him. The work will wait. Somehow it will get done. But this is my life and I don't want to look back many years from now and have regrets about things I've missed.
But, I digress. That is not the problem, albeit well known, to that I want to address today.
As 2012 winds to an end, I look back on a year of triumphs and tribulations. My oldest child graduated from high school, but quickly decided that her time was best spent traveling the countryside, jumping from one house to another. I never knew where she was or when she might call. I kept paying for her cell phone with the hopes that she would call, even though she would rarely answer my calls. Thankfully, she is back home now, with plans to attend the local community college beginning in January. Our middle child finished his senior year of football, both a happy and sad occasion following years of practices and games. The youngest had a successful first year in 4H, began playing drums in the school band, and picked up piano lessons.
So where is this headed? I am the type of person that makes to-do lists and am quick to try to delete items from said list. As teachers we know that this list is simply a cycle of making lesson plans, teaching, grading homework/tests/quizzes, answering emails, making phone calls; the list goes on and on. Clearly there are not enough hours in the school day to complete all of these tasks. Some of it must be brought home. And therein lies my problem. I find it difficult to enjoy life when I see so much work just waiting to be completed. For example, today is New Year's Eve and my husband and I have been planning a viewing of Les Miserables for the evening. But, seeing the upcoming days of school on Thursday and Friday, I find that I am more drawn to work on my lesson plans for those days. I feel the stress building up. I look back at this past year and see multiple instances of sitting through school concerts or games, but thinking not of the joyfulness around me. Rather, I am thinking of the most efficient way to accomplish the loads of work waiting for me at home. Some days, like today, I find it difficult to even think of leaving the house.
I don't know how to get past it. How do I balance the demands of my job and the life with my family? About the middle of November I decided that my life was of more importance to me. While I did pack up papers and bring them home in the evening, I rarely worked on them. I spent time watching TV with my kids, working on homemade Christmas presents, and enjoying some time alone. While this did help me feel less guilty as a parent, it also meant that I had LOADS more work to accomplish while at school. And somehow this all worked out. Time just seemed to become available.
So, I write this post not to inform you of my personal struggles, but to let others teachers (be they new or veteran) know that life should come first. Don't let your job consume your life. Enjoy every minute you have. Live in each moment, don't just be a participant. I noticed this change most at my daughter's Christmas program. I watched the faces of each child: the quirky ones, the let-me-sing-in-my-loudest-voice ones, the kids with the squeaky clarinets, and I truly saw what I had been missing all along.
So tonight the work will wait. I will grab a BOX of tissues and the hand of my loved one. I will sit in a quiet theater, most likely crying, and enjoy the moment that I have with him. The work will wait. Somehow it will get done. But this is my life and I don't want to look back many years from now and have regrets about things I've missed.
Tuesday, August 21, 2012
Change is underfoot...
I haven't written in what feels like forever. The start of school has really thrown me for a loop.
The first day of school with students was last Friday. Overall, I am blessed this year with some pretty good students. I have three sections of Geometry and one section each of Algebra 2B, Statistics and RtI. As of today, I don't have students "enrolled" in my RtI class. That will change in the upcoming weeks as the teachers start to really assess what skills the students need more work on. As for the other classes, I have about 50 total in my 3 geometry sections. These are the students that are new to me. I have previously taught most of the students that I have in Algebra 2B and Statistics. This makes it a lot less stressful to remember names. My goal is to have all the students' names in my head by the end of this week, but as I've told the students, this only means I know their names while their bodies are in their assigned seats. The recognition in the hallway will come later.
I've added a lot to my curriculum this year and am finding it difficult to get everything done on time. I feel like if I could get a week ahead things would run a lot more smoothly in my head. I've done a pretty decent job of not letting the students see that side of my fractured brain, though. I haven't taught algebra 2B for a couple of years, so the topics are "new" to me again this year. In statistics, a lot of changes have taken place. I've added interactive notebooks to my list of things to include this year. The kids LOVE them. I've heard no negativity about them, but have heard several positives. One memorable comment came from Joey when he said that the INB reminded him of the pop-up books he used to love as a kid. Several other students have also mentioned that they appreciate how the INB helps keep them organized when they are typically not that organized.
On to Statistics...
The stats class that i teach is dual credit, which means the students are earning high school credit and college credit (through a local community college) at the same time. Up until this year, I've done a pretty lame job of making the class interesting or engaging. Lessons typically consisted of notes and practice problems from the book in the past. This year, I've decided that some of those lessons need less emphasis and more should be placed on showing the students how stats is used in everybody's daily life. Here I sat with the prime example of a math class that is useful to everyone and was doing nothing with it. Shame on me!
We've started the year off with a more structured introduction to the research process - identifying who, what, when, where, why, and how for statistical studies - and are working toward how samples are collected, different types of studies and the like. I am doing this because I intend to have my students become statisticians. Shortly before school started, I emailed my principal about the possibility of having my stats kids do some data analysis for the school. A week later at the faculty meeting, the principal shocked me by telling the faculty that my stats class would do all of the data analysis for the school and would be disseminating it as needed. I am thrilled for this opportunity and scared of it at the same time.
In the same week that I sent the email to the principal, I also applied for my class to help analyze Curiousity data for the Mars rover mission. I had heard about this as a possibility through a friend and was curious to what it would entail. I heard back the following day with a message that stated the program would begin sometime in September.
Based on these two commitments, stats is about to become a much different class. This alone has me pumped (not a word I usually use) for the year ahead! I am so excited!
The first day of school with students was last Friday. Overall, I am blessed this year with some pretty good students. I have three sections of Geometry and one section each of Algebra 2B, Statistics and RtI. As of today, I don't have students "enrolled" in my RtI class. That will change in the upcoming weeks as the teachers start to really assess what skills the students need more work on. As for the other classes, I have about 50 total in my 3 geometry sections. These are the students that are new to me. I have previously taught most of the students that I have in Algebra 2B and Statistics. This makes it a lot less stressful to remember names. My goal is to have all the students' names in my head by the end of this week, but as I've told the students, this only means I know their names while their bodies are in their assigned seats. The recognition in the hallway will come later.
I've added a lot to my curriculum this year and am finding it difficult to get everything done on time. I feel like if I could get a week ahead things would run a lot more smoothly in my head. I've done a pretty decent job of not letting the students see that side of my fractured brain, though. I haven't taught algebra 2B for a couple of years, so the topics are "new" to me again this year. In statistics, a lot of changes have taken place. I've added interactive notebooks to my list of things to include this year. The kids LOVE them. I've heard no negativity about them, but have heard several positives. One memorable comment came from Joey when he said that the INB reminded him of the pop-up books he used to love as a kid. Several other students have also mentioned that they appreciate how the INB helps keep them organized when they are typically not that organized.
On to Statistics...
The stats class that i teach is dual credit, which means the students are earning high school credit and college credit (through a local community college) at the same time. Up until this year, I've done a pretty lame job of making the class interesting or engaging. Lessons typically consisted of notes and practice problems from the book in the past. This year, I've decided that some of those lessons need less emphasis and more should be placed on showing the students how stats is used in everybody's daily life. Here I sat with the prime example of a math class that is useful to everyone and was doing nothing with it. Shame on me!
We've started the year off with a more structured introduction to the research process - identifying who, what, when, where, why, and how for statistical studies - and are working toward how samples are collected, different types of studies and the like. I am doing this because I intend to have my students become statisticians. Shortly before school started, I emailed my principal about the possibility of having my stats kids do some data analysis for the school. A week later at the faculty meeting, the principal shocked me by telling the faculty that my stats class would do all of the data analysis for the school and would be disseminating it as needed. I am thrilled for this opportunity and scared of it at the same time.
In the same week that I sent the email to the principal, I also applied for my class to help analyze Curiousity data for the Mars rover mission. I had heard about this as a possibility through a friend and was curious to what it would entail. I heard back the following day with a message that stated the program would begin sometime in September.
Based on these two commitments, stats is about to become a much different class. This alone has me pumped (not a word I usually use) for the year ahead! I am so excited!
Friday, August 3, 2012
My Favorite Friday #2 - Italian Beef
My Favorite Friday started last week, but other commitments made me miss it. I did take time to read through all of the other posts, though. One in particular stood out and me - Tex Mex Chicken by @Wyldbirman. It's not a recipe I've tried yet, but will be later today. After seeing that post, I suggested to @druinok that we devote one week of My Favorite Fridays to menus that teachers/parents can use when they're horribly busy and can't find time to cook or just want an easy meal to make. With that said, here's one of our family's favorite meals.
Italian Beef
Line a crock pot with a liner (easy clean up). Cut the fat off one 3-4 lb roast and then cut the remaining meat into small cubes. Dump these pieces into the crock pot along with 1 can of beer, a jar of pepperoncini peppers, a small can of beef consumme soup, 1 tsp each of oregano and italian seasoning. Turn the crock pot on low for 8 hours or so.
I typically shred the meat afterwards with a couple of forks and serve it on hoagie rolls. My husband likes to add a little shredded mozzarella on top. Any leftover meat goes back in the juices to be used for beef and noodles. The juices/leftover meat freezes well so beef and noodles can be served at a later time.
The pepperoncini peppers do give the meat a bit of spice, but it is not so hot that kids won't eat it. You can control how hot you want it to be by not using the whole jar in the mix. You may also want to pull out a few of the peppers before adding to the crock pot if you would like to have them with the sandwich later. While you can still eat the peppers after they've been cooked, they are quite limp.
Sunday, July 29, 2012
Common Core Geometry
This #made4math project is a little out of the ordinary compared to the other crafty projects that I've done. But, out of all the projects that I've done this was is the most useful to my classroom thus far.
Last Friday, I went to school to work for a couple of hours. Seven hours later (yep you read that write) I left exhausted, but feeling accomplished. Initially I spent time setting up my Promethean Board, which I had no experience with as it was installed last October. Unfortunately, there were some issues that took a little while to deal with (and are still not completely fixed). But, the better part of my day was spent organizing the Common Core State Standards for geometry.
I started by cutting apart the standards and then trying to shuffle them around on a desk. I found this difficult to track as a whole course and changed to organizing the units on the whiteboard that spans about 16 feet on my back wall. Ultimately I ended up with 10 units, but have since changed this to 11 units.
I should state that this is a process that I went through last summer as well. For whatever reason, the results that I ended up with then didn't feel "right", so I set them aside and went on teaching with just a few deviations from my usually path.
So after several hours of thinking, writing, interpreting, and erasing, here's what I developed.
Unit 1: Review, Introduction of geometry terminology & notation
Standards: CO.1, CO.9, CO.10, GPE.5, GPE.7, MG.1
Unit 2: Rigid Transformations
Standards: CO.2, CO.3, CO.4, CO.5, CO.6
Unit 3: Congruence and Triangles
Standards: CO.6, CO.7, CO.8, CO.9, CO.10, CO.12, GPE.4
Unit 4: Triangle Centers
Standards: CO.10, CO.13, C.2, C.3
*I hope to introduce the relationships between inscribed and central angles, and possibly touch on angles created by two tangent lines to a circle. (present when constructing perpendicular and angle bisectors) My goal is to make those angle measure relationships easier to remember when all the other angle and chord "rules" are added when we discuss circles.
Unit 5: Quadrilaterals
Standards: CO.11, GPE.4
Unit 6: Circles
Standards: GPE.1, GPE.4, C.2, C.4
Unit 7: Similarity
Standards: SRT.1, SRT.2, SRT.3, C.1, C.5
Unit 8: Proofs & Similarity
Standards: SRT.4, SRT.5, CO.10, GPE.4
Unit 9: Trigonometry
Standards: SRT.6, SRT.7, SRT.8, SRT.9, SRT.10, SRT.11
Unit 10: Solid Geometry
Standards: GMD.1, GMD.3, GMD.4, MG.1, MG.2, MG.3
Unit 11: Prob & Stats
Standards: CP.1-CP.9, MD.6, MD.7
For the most part these units follow the lead given in Appendix A to the CCSS, but I feel that these are in groups that I think will make teachable groups.
Now for the more time-consuming task of making up lessons, objectives for standards based grading, quizzes, tests, etc.
Last Friday, I went to school to work for a couple of hours. Seven hours later (yep you read that write) I left exhausted, but feeling accomplished. Initially I spent time setting up my Promethean Board, which I had no experience with as it was installed last October. Unfortunately, there were some issues that took a little while to deal with (and are still not completely fixed). But, the better part of my day was spent organizing the Common Core State Standards for geometry.
I started by cutting apart the standards and then trying to shuffle them around on a desk. I found this difficult to track as a whole course and changed to organizing the units on the whiteboard that spans about 16 feet on my back wall. Ultimately I ended up with 10 units, but have since changed this to 11 units.
I should state that this is a process that I went through last summer as well. For whatever reason, the results that I ended up with then didn't feel "right", so I set them aside and went on teaching with just a few deviations from my usually path.
So after several hours of thinking, writing, interpreting, and erasing, here's what I developed.
Unit 1: Review, Introduction of geometry terminology & notation
Standards: CO.1, CO.9, CO.10, GPE.5, GPE.7, MG.1
Unit 2: Rigid Transformations
Standards: CO.2, CO.3, CO.4, CO.5, CO.6
Unit 3: Congruence and Triangles
Standards: CO.6, CO.7, CO.8, CO.9, CO.10, CO.12, GPE.4
Unit 4: Triangle Centers
Standards: CO.10, CO.13, C.2, C.3
*I hope to introduce the relationships between inscribed and central angles, and possibly touch on angles created by two tangent lines to a circle. (present when constructing perpendicular and angle bisectors) My goal is to make those angle measure relationships easier to remember when all the other angle and chord "rules" are added when we discuss circles.
Unit 5: Quadrilaterals
Standards: CO.11, GPE.4
Unit 6: Circles
Standards: GPE.1, GPE.4, C.2, C.4
Unit 7: Similarity
Standards: SRT.1, SRT.2, SRT.3, C.1, C.5
Unit 8: Proofs & Similarity
Standards: SRT.4, SRT.5, CO.10, GPE.4
Unit 9: Trigonometry
Standards: SRT.6, SRT.7, SRT.8, SRT.9, SRT.10, SRT.11
Unit 10: Solid Geometry
Standards: GMD.1, GMD.3, GMD.4, MG.1, MG.2, MG.3
Unit 11: Prob & Stats
Standards: CP.1-CP.9, MD.6, MD.7
For the most part these units follow the lead given in Appendix A to the CCSS, but I feel that these are in groups that I think will make teachable groups.
Now for the more time-consuming task of making up lessons, objectives for standards based grading, quizzes, tests, etc.
Friday, July 27, 2012
#TMC12
I wish I could get this blog post to flow, but I have WAY too much stuff to say...
As far as online things go, I'm a noob. While I've stalked other people's blogs for about 2 years, I've only been involved in the Twitter community for about a month. Initially Twitter was not in my plans. I thought I had enough going on and that adding another site to my already too long sessions online was a waste of time. I spend plenty of it on Facebook, G Reader, & Pinterest as is. But, I digress.
So how'd I end up a Twitter Math Camp? In one of the blog posts written by @druinok I read a statement that resonated with me. In essence she stated that she was disappointed with professional development opportunities and mentioned Twitter Math Camp. So I did what any inquisitive person would do....I googled it. This led me to the registration page for the camp. Keep in mind that at this point I still did not possess a Twitter ID. I spent the next week relaying to my husband that I thought I might like to go. He began asking simple questions that made me realize I needed to at least sign up for Twitter and find out more info. Fast forward about 1.5 months and I'm in the group pic above. CRAZY!
So, what have I learned? First and foremost, this group of people that I am now involved with on Twitter is a group that is devoted to doing the best job at teaching mathematics (to kids at all grade levels) that they can possibly do. They share stories, successes and failures, ideas, give advice, among other things. But they are also a group of individuals that share parts of their lives with each other as if they simply taught in the next room down the hall. The sense of camaraderie is unbelievable, especially given that most of them have never met in person.
This last fact made my going to TMC12 a little more nerve-racking. Here I am, a complete novice as far as Twitter is concerned, having amassed a total of about 225 Tweets before the conference began, attending with a group of people that "know" each other. I even asked my husband as I was packing "What if they don't like me?" His response, "You can get off Twitter and never speak to them again?" Thankfully, that wasn't necessary.
I now have a group of people that I consider friends - or Twerps - that I can bounce ideas off of, borrow ideas from, encourage, etc. It's amazing what you can find when you don't even realize you're looking!
Thank you #TMC12 for being such a change for the better in my life. (Apparently the flow eventually came to me.)
So how'd I end up a Twitter Math Camp? In one of the blog posts written by @druinok I read a statement that resonated with me. In essence she stated that she was disappointed with professional development opportunities and mentioned Twitter Math Camp. So I did what any inquisitive person would do....I googled it. This led me to the registration page for the camp. Keep in mind that at this point I still did not possess a Twitter ID. I spent the next week relaying to my husband that I thought I might like to go. He began asking simple questions that made me realize I needed to at least sign up for Twitter and find out more info. Fast forward about 1.5 months and I'm in the group pic above. CRAZY!
So, what have I learned? First and foremost, this group of people that I am now involved with on Twitter is a group that is devoted to doing the best job at teaching mathematics (to kids at all grade levels) that they can possibly do. They share stories, successes and failures, ideas, give advice, among other things. But they are also a group of individuals that share parts of their lives with each other as if they simply taught in the next room down the hall. The sense of camaraderie is unbelievable, especially given that most of them have never met in person.
This last fact made my going to TMC12 a little more nerve-racking. Here I am, a complete novice as far as Twitter is concerned, having amassed a total of about 225 Tweets before the conference began, attending with a group of people that "know" each other. I even asked my husband as I was packing "What if they don't like me?" His response, "You can get off Twitter and never speak to them again?" Thankfully, that wasn't necessary.
I now have a group of people that I consider friends - or Twerps - that I can bounce ideas off of, borrow ideas from, encourage, etc. It's amazing what you can find when you don't even realize you're looking!
Thank you #TMC12 for being such a change for the better in my life. (Apparently the flow eventually came to me.)
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