I consistently find that students struggle with scale when graphing. They often can't quite wrap their heads around a graph that has a scale other then 1 to 1, or when the x and y axis have vastly different scales. Also, when setting up scales, students will not make the space between their labels consistent. For example, if labeling the y-axis by 10s, the student may skip one square on the graph paper, and label it five, but then skip two squares for each 10 after that.
I felt frustrated that I didn't have a resource that asked students to practice JUST making scale, so I've developed my own series of activities for them to practice that. This is designed to be used with gradual release. Do the first couple activities on the doc cam as an entire class, then have the students work with a partner on the next few.
Finally have the students work individually to set up graphs from the final page. They don't have to graph the points/lines, since the learning objective is to create a workable, accurate scale for both the x- and y-axis based on the data given, but of course if students need or want to practice the graphing, they can do that too.
Here's the worksheets I made to practice this: Graphing: Practicing Scale
Showing posts with label math. Show all posts
Showing posts with label math. Show all posts
Friday, February 19, 2016
Saturday, January 24, 2009
A flashlight in the dark
I finally got a few minutes to talk to Danny, my co-op teacher about my unit (which will probably be starting February 9th). Unfortunately, he doesn't really know much about it. In general the math curriculum, well, doesn't exist. I think that this is the first year that he has taught geometry here and there aren't many/any resources that the school has. As a policy, the school doesn't use text books. This is both a philosophical and a monetary decision, I believe, and I appreciate what they are going for with that. Too often it seems like teachers take a text book as curriculum whole sale, and just go through the book with little to no supplementing. This can be a particular mistake with students that are similar to the ones at A3. As an arts high school, a lot of the students have math phobia (and many of the teachers too). In an effort to draw in those students, and help them to appreciate and enjoy math, most of the instruction is inquiry or project based. The problem being that as of yet, there aren't any existing lesson plans or projects, or even sources for problems for me to draw from. Maybe I'll go buy a Geometry text book from Smith Family, just to use as a resource for equations/problems, I already have an Algebra and a Calculus book.
Danny walked me through how a typical day goes for them in math. He says they like to start with a warm up or brain teaser, and then move into explaining and discussing the concepts they'll be working with. He didn't really go into any specifics as to how that is usually done. Definitions and vocabulary are usually a large focus for the students, as that is often what holds them back from understanding what is going on. After the concepts are addressed, the students break into small groups and work on figuring out one or two problems. After they have had a period of time to work, and come up with a solution, each group shares what they did and how/why they did it. This, Danny said, is often the most difficult part for students, the explanation of why thy do certain steps. It seems like there is a general 'no homework' policy, though I'm not sure if that is just these particular teacher's philosophy, or a school wide policy. In general I don't think that assigning tons of homework is necessary, however, allowing students an opportunity to work on the math concepts in a different space, without the resources of their friends and teachers can be a great learning experience. On the other hand, I was just reading an article for my Curriculum Assessment Alignment class that was discussing the fact that school trains students for a type of work that is not often found in the real world. How often would a person have to do computations without the aid of a peer or adviser, outside of academic and assessment situations?
So now my task is to search for problems, vocab and brain teasers for dealing with quadrilaterals, and find a way to integrate them into the culture of the math classroom, without ever actually seeing that culture. Not to mention make sure that those materials and goals are aligned with the content standards for Geometry. This is definitely a new challenge.
Danny walked me through how a typical day goes for them in math. He says they like to start with a warm up or brain teaser, and then move into explaining and discussing the concepts they'll be working with. He didn't really go into any specifics as to how that is usually done. Definitions and vocabulary are usually a large focus for the students, as that is often what holds them back from understanding what is going on. After the concepts are addressed, the students break into small groups and work on figuring out one or two problems. After they have had a period of time to work, and come up with a solution, each group shares what they did and how/why they did it. This, Danny said, is often the most difficult part for students, the explanation of why thy do certain steps. It seems like there is a general 'no homework' policy, though I'm not sure if that is just these particular teacher's philosophy, or a school wide policy. In general I don't think that assigning tons of homework is necessary, however, allowing students an opportunity to work on the math concepts in a different space, without the resources of their friends and teachers can be a great learning experience. On the other hand, I was just reading an article for my Curriculum Assessment Alignment class that was discussing the fact that school trains students for a type of work that is not often found in the real world. How often would a person have to do computations without the aid of a peer or adviser, outside of academic and assessment situations?
So now my task is to search for problems, vocab and brain teasers for dealing with quadrilaterals, and find a way to integrate them into the culture of the math classroom, without ever actually seeing that culture. Not to mention make sure that those materials and goals are aligned with the content standards for Geometry. This is definitely a new challenge.
Wednesday, October 15, 2008
Word Processing; likes and dislikes
Unti planning is chugging along. I wrote my pre-test yesterday. I ran into a problem that I'm sure plagues math teachers everywhere. How DO you write equations in Microsoft Word? Are there special math word processing programs that you can use in order to write these things? Now I know why my tests in calculus were always hand written by my teacher. Fortunately I have decent handwritting, so in the future I might choose to take that route. For the time being however, and the perception of proffessionalism I will continue to try and type them. The pretest required nothing more complicated then fractions and division signs. But I could not figure out any way to make the fractions be vertically aligned rather then on a diagonal from one another. Which is no big deal in every days use, but when you are teaching students the algorithms for multiplying and dviiding fractions (or even adding and subtraction) having a clear sense of top and bottom is key.
I am starting to get a clear list of things that I do and don't want in my classroom. I love the expectations from teh begining. Having the students help compile them. I even sort of like the 'give me five' thing, although I don't prefer it to just generally respecting one another. It's better then shouting. I like the use of comedy and humor that Mrs. Keener uses, she is goofy and silly and makes things fun.
Things I don't like so much, or would do differently: As I've mentioned before, if I ask for questions from students, they will not be allowed to make comments. They should know the difference between questions and comments by now. I also have noticed that sometimes Mrs. Keener makes a big deal out of things that would be less important to me. For instance she criticized one student for having doodles on her homework, or for putting the homework problems in rows instead of in collumns. Another thing that hs be driving me nuts is that there is no generic place where the keys to homework sheets we've done go. I assume this is because Mrs. Keener has been working with the same materials for many years, and she knows where she keeps them. However, when I am dong something like grading late work, and she has already put the key back, I have no idea whre to find it. I think a good play would be to have a binder where all of the keys for the worksheets done each term were kept. They would only be replaced to their fiile after that assignment was no longer going to be accepted as late. Be that the end of the week, the month or the term. I also think that in addition to graded work, I would choose to give students some sort of participation points for being present. Mrs. Keener sort of does this with the warm-up. Students get credit for simply having done the warm up, I like that, and would choose to do somethign similar. But students who are absent do not get marked down on the warm up. With participation points, it would reward those student who were in class every day, even if they didn't necessarily do well on their homework or tests. I have had classes that do this both in Middle/High school and in college and I think it is an effective way to help level the playing field as far as grades are concerned.
I am also not a huge fan of the way that the late policy works here at Briggs. It is something that has been agreed upon by all the sixth grade teachers. Management is the biggest issue with late work. How do you know when a student turned something in? I would perhaps get one of those old-school date stamps like libraries used to have, and when a student turns in some work, they would have to get it stamped, or they would recieve no credit. One day late would be one grade off, two days would be two grades, etc. Depending on the age, late work would either stop being accepted after a week or so (except in special circumstances, this policy would be for older students) or would recieve a maximum of half credit if it is later then a given date, but still be accepted (for 6th and maybe 7th graders, as the continue to try and make that transition from elementary to middle school). This isn't a perfect policy, I would have to do some polishing. If I were in a position to be teaching Pre-Calc or Calc, I don't think I would accept late work at all, except in the case of absence. But then again. I also don't like grading homework. I don't know if this would be functional with Middle School age students, unless it was perhaps with the advanced group, but I would like to assign homework questions, but not have them be turned in or required. That way students did homework if they needed to. The day homework was 'due' the students would have opportunity to ask questions, and then we would move on. Grades would be based upon participation points, tests, quizes, and projects. This was the way my favorite math classes have always functioned.
Between my Behavior Management class and the student teaching, I feel like I am starting to come up with a coherent personal policy/philosophy, which I suppose is the point.
I am starting to get a clear list of things that I do and don't want in my classroom. I love the expectations from teh begining. Having the students help compile them. I even sort of like the 'give me five' thing, although I don't prefer it to just generally respecting one another. It's better then shouting. I like the use of comedy and humor that Mrs. Keener uses, she is goofy and silly and makes things fun.
Things I don't like so much, or would do differently: As I've mentioned before, if I ask for questions from students, they will not be allowed to make comments. They should know the difference between questions and comments by now. I also have noticed that sometimes Mrs. Keener makes a big deal out of things that would be less important to me. For instance she criticized one student for having doodles on her homework, or for putting the homework problems in rows instead of in collumns. Another thing that hs be driving me nuts is that there is no generic place where the keys to homework sheets we've done go. I assume this is because Mrs. Keener has been working with the same materials for many years, and she knows where she keeps them. However, when I am dong something like grading late work, and she has already put the key back, I have no idea whre to find it. I think a good play would be to have a binder where all of the keys for the worksheets done each term were kept. They would only be replaced to their fiile after that assignment was no longer going to be accepted as late. Be that the end of the week, the month or the term. I also think that in addition to graded work, I would choose to give students some sort of participation points for being present. Mrs. Keener sort of does this with the warm-up. Students get credit for simply having done the warm up, I like that, and would choose to do somethign similar. But students who are absent do not get marked down on the warm up. With participation points, it would reward those student who were in class every day, even if they didn't necessarily do well on their homework or tests. I have had classes that do this both in Middle/High school and in college and I think it is an effective way to help level the playing field as far as grades are concerned.
I am also not a huge fan of the way that the late policy works here at Briggs. It is something that has been agreed upon by all the sixth grade teachers. Management is the biggest issue with late work. How do you know when a student turned something in? I would perhaps get one of those old-school date stamps like libraries used to have, and when a student turns in some work, they would have to get it stamped, or they would recieve no credit. One day late would be one grade off, two days would be two grades, etc. Depending on the age, late work would either stop being accepted after a week or so (except in special circumstances, this policy would be for older students) or would recieve a maximum of half credit if it is later then a given date, but still be accepted (for 6th and maybe 7th graders, as the continue to try and make that transition from elementary to middle school). This isn't a perfect policy, I would have to do some polishing. If I were in a position to be teaching Pre-Calc or Calc, I don't think I would accept late work at all, except in the case of absence. But then again. I also don't like grading homework. I don't know if this would be functional with Middle School age students, unless it was perhaps with the advanced group, but I would like to assign homework questions, but not have them be turned in or required. That way students did homework if they needed to. The day homework was 'due' the students would have opportunity to ask questions, and then we would move on. Grades would be based upon participation points, tests, quizes, and projects. This was the way my favorite math classes have always functioned.
Between my Behavior Management class and the student teaching, I feel like I am starting to come up with a coherent personal policy/philosophy, which I suppose is the point.
Sunday, October 12, 2008
Meetings and the Commencement of my unit planning!
I am having a difficult time readjusting to a busy life in which many things are badgering for my attention. Currently my personal life, and my practicum are where I am most inclined to spend time and energy, and I'm finding it difficult to give focus to my class work, despite the fact that the class work is what had eminent deadlines. Along that strain, I left my notebook with my observation notes at school, which is making it a bit of a challenge to write a thoroughly thought through reflection for the week.
One thing that is fresh in my mind is the (two actually) meetings I had on Friday. I normally don't come into school on Fridays, and had come specially for a meeting about the new curriculum that I will be teaching from. It also so happens that there was an intervention type meeting for a student in my class who has been having trouble. I sat in on that and found it enlightening to say the least. I know that I personally find that I am most dreading ( about teaching) the interaction with parents. I'm afraid I won't gracefully put up with parents who think their children are God's gift to the entire world (not just them.) Or the parents who expect me, as a teacher of a class of thirty, to change my entire teaching style/structure/whatever in order to suit their student. However, the parents of this particular kid were great. Without getting angry or placing blame on the student, they acknowledged that he had issues and challanges. They made a point of saying that they didn't expect teachers to change the way they taught, but were seeing help from the school to make the transition from elementary school to high school a bit easier on their child. The meeting was really positive, there was praise for the student as well as discussion of his problems, and after discussion from/with all of his teachers, the counselor helped to create a specific plan for how improvement could be made. I was surprised (though I suppose I shouldn't be) how much behind the scenes decision making there can be. For instance this student has some interpersonal issues in some classes, but not in others. So he is creating a list of those students he wants to sit by, and can work well with, and those students he really doesn't want to sit near, so that the teachers can arrange him in a group situation in which he can be successful. I would never have thought of straight up asking the student who he wanted to sit with. That seems so... unfair. But if this student is able to work positively in that group, then that will allow the other students to work without the disruption he was previously causing.
After that meeting, we had out curriculum meeting and I got my first taste of the headache that teachers have to go through to match their curriculum up. We have a new set of 'focal points' that we have to hit, in a certain order. And a district mandated schedule for how long should be spent on each focal point, and what your advanced and lower group should be doing, and when you should be working with both groups together etc. It was such a headache. Not only that, but the text book we are using doesn't match up with the state standards. Things are grouped differently, there are sub-chapters on things we don't need to cover. It was mind-boggling, and I can't say enough how grateful I am to have these two veteran teacher to work with on writing my unit plan. I especially appreciate how both of these teachers (Mrs. Keener, and Mr. Smith) treat me as a peer, a peer with less experience, but they don't talk down to me, or try and cut me out of things. They go out of their way to include me in all relevant conversations so that I get a true experience.We have a real pedagogical challenge in that our classes are heterogeneous, but we are expected to teach differentiated lessons to the high and low students. So there will be student swapping and team teaching, it will be really important that we stay at the same speed as we move through the chapters. Part of the focal point plan is that each subject is learned to mastery, so I am going to have to be creative to find ways to continue to work on multiplying and dividing fractions without boring the students (or myself!) After an hour or so, and a long phone call to the principal, we started to get things hammered out. I now know that I will be teaching a unit on converting between fractions and decimals, and then multiplying and dividing decimals. I will start my unit on Monday October 27th, and we plan for it to be four weeks long.
One thing that is fresh in my mind is the (two actually) meetings I had on Friday. I normally don't come into school on Fridays, and had come specially for a meeting about the new curriculum that I will be teaching from. It also so happens that there was an intervention type meeting for a student in my class who has been having trouble. I sat in on that and found it enlightening to say the least. I know that I personally find that I am most dreading ( about teaching) the interaction with parents. I'm afraid I won't gracefully put up with parents who think their children are God's gift to the entire world (not just them.) Or the parents who expect me, as a teacher of a class of thirty, to change my entire teaching style/structure/whatever in order to suit their student. However, the parents of this particular kid were great. Without getting angry or placing blame on the student, they acknowledged that he had issues and challanges. They made a point of saying that they didn't expect teachers to change the way they taught, but were seeing help from the school to make the transition from elementary school to high school a bit easier on their child. The meeting was really positive, there was praise for the student as well as discussion of his problems, and after discussion from/with all of his teachers, the counselor helped to create a specific plan for how improvement could be made. I was surprised (though I suppose I shouldn't be) how much behind the scenes decision making there can be. For instance this student has some interpersonal issues in some classes, but not in others. So he is creating a list of those students he wants to sit by, and can work well with, and those students he really doesn't want to sit near, so that the teachers can arrange him in a group situation in which he can be successful. I would never have thought of straight up asking the student who he wanted to sit with. That seems so... unfair. But if this student is able to work positively in that group, then that will allow the other students to work without the disruption he was previously causing.
After that meeting, we had out curriculum meeting and I got my first taste of the headache that teachers have to go through to match their curriculum up. We have a new set of 'focal points' that we have to hit, in a certain order. And a district mandated schedule for how long should be spent on each focal point, and what your advanced and lower group should be doing, and when you should be working with both groups together etc. It was such a headache. Not only that, but the text book we are using doesn't match up with the state standards. Things are grouped differently, there are sub-chapters on things we don't need to cover. It was mind-boggling, and I can't say enough how grateful I am to have these two veteran teacher to work with on writing my unit plan. I especially appreciate how both of these teachers (Mrs. Keener, and Mr. Smith) treat me as a peer, a peer with less experience, but they don't talk down to me, or try and cut me out of things. They go out of their way to include me in all relevant conversations so that I get a true experience.We have a real pedagogical challenge in that our classes are heterogeneous, but we are expected to teach differentiated lessons to the high and low students. So there will be student swapping and team teaching, it will be really important that we stay at the same speed as we move through the chapters. Part of the focal point plan is that each subject is learned to mastery, so I am going to have to be creative to find ways to continue to work on multiplying and dividing fractions without boring the students (or myself!) After an hour or so, and a long phone call to the principal, we started to get things hammered out. I now know that I will be teaching a unit on converting between fractions and decimals, and then multiplying and dividing decimals. I will start my unit on Monday October 27th, and we plan for it to be four weeks long.
Monday, September 29, 2008
Long busy day
Today was the first day of my classes, and I anticipated a bit more stress then usual. Today was particularly unique, however, because Mrs. Keener was unexpectedly sick. She came in long enough to leave a lesson for me and the sub, but that was it. She was gone by the time I got there at 9:30. I also didn't realize that she was not in the building until the sub walked in, five minutes before the kids arrived. I figured she was at a meeting, or off in another part of the bulding taking care of something. When the sub suggested that I teach the lesson, since I probably under stood the math better then he did, I readily consented, but I didn't even get to fully read the lesson plan before it was time to start! Talk about teaching on the fly. I made up a warm-up off the top of my head, with a little input from students as to what they wanted to practice, and set about teaching the lesson on using rectangular arrays to factor. Fortunately this is something which I am pretty familiar with, so the lesson was no problem. Although I originally made the mistake of handing out the square 'chips' before I went over the worksheet, so a lot of kids lost out on the instruction because they were playing with the manipulatives. I did that differently when I taught it in the afternoon. Kids also were having a hard time interpreting the analysis questions on the back (heck, some of those questions were complicated for me!) so I am concerned that they will be unable to complete it by tomorrow. I think I did pretty well with the teaching considering the total lack of preperation. The kids like me and respect me, and follow my directions pretty well. Being at a middle school, I am clearly 'one of them' to the kids. They don't identify with me as a young person, they identify with me as an adult, although I'm sure they recognize that I am younger then Mrs. Keener. Especially some of the more 'problematic' boys seem to have taken to me. I'm not sure what it is about that. If it's the fact that I take the time to give them some appropriate attention, if it's that I laugh at their jokes (when it's the appropriate time and the jokes are good) or what. But three boys in particular who give Mrs. Keener (and their other core teacher) a lot of trouble, behave pretty well for me, though they do need reminding from time to time. Perhaps I'm just new and exciting? One particularly good lesson for today is that I need to pay more attention to time when I am teaching. I accidently spent nearly half of math on the warm-up, and the science lesson took way longer then Mrs. Keener had indicated it should have. Although when the sub taught science, in the afternoon, it took them the same amount of time it took me.
Mrs. Keener has told me, and other teachers have confirmed this, that one of my strongest traits as a pre-service teacher is my confidence. Someone asks me if I can do something, and my response is nearly always "sure, no problem". I hope that this confidence I have doesn't balloon into over-confidence though. I would hate to get in over my head.
I had one other really interesting interaction today. We were working in groups on math and one boy came up to me with two questions. He's a kid who is pretty quiet and is often sort of zoning out. His first question had to do with the requirements for a science project that is due on Wednesday. The second question totally took me by surprise. He asked, " If humans evolved from monkeys, why are there still monkeys?" A very analytical question from a person who I hadn't given enough credit! ( Not to mention compleatly off topic, and having nothing to do with anything we were doing in class, science or otherwise). I took a second, and told him about a story I'd heard about butterflys changing their spots to match thier environment when a factory producing lots of ash was built in their habitat, while the butterflys of the same speciies that didn't live near the factory didn't develop spots. I don't remember where i heard this anecdote, but it's always stuck with me. So, I explained, perhaps the monkeys that are still monkeys didn't have something making an evolution necessary. I wish I'd come up with something better, evolution isn't something I am terribly familiar with. My knoweldge steming a little from Freshman biology, and a little from the book Sophie's World, where they touch on it from a philosophical point of view.
All in all a full day. I can't wait to see what the rest of the week has in store. We are going to 'sky camp' on Thursday to do some team building. Sounds exciting!
Mrs. Keener has told me, and other teachers have confirmed this, that one of my strongest traits as a pre-service teacher is my confidence. Someone asks me if I can do something, and my response is nearly always "sure, no problem". I hope that this confidence I have doesn't balloon into over-confidence though. I would hate to get in over my head.
I had one other really interesting interaction today. We were working in groups on math and one boy came up to me with two questions. He's a kid who is pretty quiet and is often sort of zoning out. His first question had to do with the requirements for a science project that is due on Wednesday. The second question totally took me by surprise. He asked, " If humans evolved from monkeys, why are there still monkeys?" A very analytical question from a person who I hadn't given enough credit! ( Not to mention compleatly off topic, and having nothing to do with anything we were doing in class, science or otherwise). I took a second, and told him about a story I'd heard about butterflys changing their spots to match thier environment when a factory producing lots of ash was built in their habitat, while the butterflys of the same speciies that didn't live near the factory didn't develop spots. I don't remember where i heard this anecdote, but it's always stuck with me. So, I explained, perhaps the monkeys that are still monkeys didn't have something making an evolution necessary. I wish I'd come up with something better, evolution isn't something I am terribly familiar with. My knoweldge steming a little from Freshman biology, and a little from the book Sophie's World, where they touch on it from a philosophical point of view.
All in all a full day. I can't wait to see what the rest of the week has in store. We are going to 'sky camp' on Thursday to do some team building. Sounds exciting!
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