As I look at materials and make plans for next year, I have come to the conclusion that there is something else I want...
I want good questions. I want the kinds of questions which will make my students interested in figuring out why something is true. I want the kinds of questions which catch the class' attention and keep them thinking about math well after the bell has rung.
Here's my problem, though, I don't want to be the only person asking these questions. I want my students asking these questions. I want to end class at least once a week not even knowing the answer(s) to these questions myself.
They say in government that you subsidize what you want more of and tax what you want less of. I need to subsidize inquiry.
I am planning on introducing the creation and use of an interactive notebook in my Algebra 2 classes. I have been thinking about how to use the left-side of the notebook. I've asked friends on twitter (hello: @mgolding @algebraniac1 @druinok @reilly0141 I think those are the peeps with whom I discussed INB's on Tuesday). I also reviewed the Global Math Department recording from a couple weeks ago where INB's were discussed.
Formats for the left sides are pretty fluid, leaving the options very open. I know that I plan on having students reflect on topics in that section. I also want to encourage asking good questions there. I generally try to not pay off students with candy (erasers, etc) too often, but I want good questions and deep thought too much to not consider the use of bribery to get it.
I have started mapping out my first couple units in the INB (well, the right-hand sides). I will be reading, asking and thinking about how to utilize that left side. I'll share my thoughts once I reach a comfortable place with how I am envisioning that part of the notebook.
liebster award
Friday, July 12, 2013
Tuesday, July 9, 2013
What should the first day of school look like?
OR....What should the first day of school NOT look like.
I promise I will not: read through the syllabus
I promise I will not: lecture on day 1, not even rules!
I promise not to waste any time assigning seats.
I promise I will not: give a written assessment of any kind, not even an evaluatory/prescriptive one
I promise to: DO MATH
I promise to: make the kids think
I promise to : DO MATH
I promise to: challenge the students in an engaging fashion with something they can find an entry into which may or may not tie into something they might see again in class.
I have a hint at what I'm teaching, my letter of guarantee of employment for next school year only said that I would be a math teacher at (XXX) High School. (my certifications potentially allow me to teach math or ELA at middle or high school). I did speak to an administrator who did say that as things were (at the time of the discussion) that it was likely I was teaching Algebra 2 and Statistics.
In my school, Algebra 2 can be a class Freshmen are placed into, and I know I had a couple classes last year (I also taught Alg2 then as well) that were primarily Freshmen. I, actually won't know who is in my classes until the weekend before the first day of classes.
I want to start off with an activity like 4-squares, as mentioned on Mary Dooms blog (July 1st, 2013). I will have my desks set up in pairs (33 kids per class, 15 pairs and 1 triple). I want the students trying and sharing with their partners and then discussing with the class. Then I want a meatier challenge. I'm currently leaning towards Matt Vaudrey's Mullet Lesson (The only lesson they'll remember). My goal isn't evaluation, its setting a tone of exploration and risk taking with the math (in a fun way). I've got to speak to a couple of my colleagues about having prepared measurement cards and being willing to have their class interrupted to give them out.
I have 73 minutes, so I'm thinking I can at least get through enough of the mullet lesson to make it interesting. I'll let the lesson spill into the next day just a little, even if only to get them writing about the thinking process. (besides, one of the two days we'll be getting books - sad when I barely use them except for homework).
What goals do other teachers have in their lessons for the first day of school? I remember only 1 such lesson from my high school years (too long ago...). This particular teacher came in, had us write on the first page of our notebooks 3 pieces of information: a date, a phone number and Peanut M&M's. (his birthday, his phone number and his favorite candy. He got bags and bags of them on that date. Maybe he was onto something...
I promise I will not: read through the syllabus
I promise I will not: lecture on day 1, not even rules!
I promise not to waste any time assigning seats.
I promise I will not: give a written assessment of any kind, not even an evaluatory/prescriptive one
I promise to: DO MATH
I promise to: make the kids think
I promise to : DO MATH
I promise to: challenge the students in an engaging fashion with something they can find an entry into which may or may not tie into something they might see again in class.
I have a hint at what I'm teaching, my letter of guarantee of employment for next school year only said that I would be a math teacher at (XXX) High School. (my certifications potentially allow me to teach math or ELA at middle or high school). I did speak to an administrator who did say that as things were (at the time of the discussion) that it was likely I was teaching Algebra 2 and Statistics.
In my school, Algebra 2 can be a class Freshmen are placed into, and I know I had a couple classes last year (I also taught Alg2 then as well) that were primarily Freshmen. I, actually won't know who is in my classes until the weekend before the first day of classes.
I want to start off with an activity like 4-squares, as mentioned on Mary Dooms blog (July 1st, 2013). I will have my desks set up in pairs (33 kids per class, 15 pairs and 1 triple). I want the students trying and sharing with their partners and then discussing with the class. Then I want a meatier challenge. I'm currently leaning towards Matt Vaudrey's Mullet Lesson (The only lesson they'll remember). My goal isn't evaluation, its setting a tone of exploration and risk taking with the math (in a fun way). I've got to speak to a couple of my colleagues about having prepared measurement cards and being willing to have their class interrupted to give them out.
I have 73 minutes, so I'm thinking I can at least get through enough of the mullet lesson to make it interesting. I'll let the lesson spill into the next day just a little, even if only to get them writing about the thinking process. (besides, one of the two days we'll be getting books - sad when I barely use them except for homework).
What goals do other teachers have in their lessons for the first day of school? I remember only 1 such lesson from my high school years (too long ago...). This particular teacher came in, had us write on the first page of our notebooks 3 pieces of information: a date, a phone number and Peanut M&M's. (his birthday, his phone number and his favorite candy. He got bags and bags of them on that date. Maybe he was onto something...
Sunday, July 7, 2013
Pascal's Triangle, Binomial Expansion, Combinations
Looking at the probability unit (which in my classes will be the second unit we work on in the first trimester), I am trying to think of a way to show the parallels between binomial expansion, Pascal's triangle and combinations. In previous years much of this was just given to the students. (its only my second year teaching this and I took cues from what had been done before in many cases).
I'm considering a stations activity, but one in which groups are assigned to a station and work on it on a large sized whiteboard, and then without erasing a thing, they will be switched to another of the stations to see what has been done before and hopefully add to it. When completed, the groups will post their whiteboards (with 2 additional ones whose use will be apparent in time) for a gallery walk (which is when those two other boards should be completed)
I have individual sized whiteboards that I purchased a couple years back and last year we got the school to get us Home Depot boards which we had cut down to 2' x 4' size for group work.
I see one group, being given the pattern for Pascal's Triangle. (this should be a group of students who need a lower level introduction to the mathematics we will be doing). Two other groups will split up the combinations (evens one group, odds the other). Two other groups will work on binomial expansion of (x+y) with one group again doing evens and the other odds. Ideally, weaker students will get the chance to rotate from the Pascal's Triangle station to both of the other problems. Stronger students should be ok with only seeing Pascal's Triangle from in the Gallery walk.
I see the groups set up as 1. Pascal's Triangle (weaker), 2. Binomial expansion evens, 3. combinations odds, 4. binomial expansion odds, 5 combinations evens
Thoughts: I like the notion of being able to differentiate the work, with weaker students getting a view of all three procedures. I like that I'm not just showing them these things and doing a "taah-daah!" I like the idea of giving my strongest students the chance to practice distribution on a bigger problem, and have it not be busywork. I worry that I'll just get people putting (x+y)^4 = x^4 +y^4 . I'm thinking that showing the parallels for 7 rows should be sufficient and provide the students with enough practice of the skills I want. I have a germ of an idea about having students "see" the differences between permutations and combinations using differently colored beads. Maybe I can use something from that idea (which should come before this one) to flesh out the work being done by the combinations groups?
I have been trying to get the students to produce something personal to go along with these kinds of explorations (otherwise they don't remember the reason for the activity a week later) This is still something I haven't really done on this idea yet, though I'm sure I'll think of something or something will be suggested.
I'm considering a stations activity, but one in which groups are assigned to a station and work on it on a large sized whiteboard, and then without erasing a thing, they will be switched to another of the stations to see what has been done before and hopefully add to it. When completed, the groups will post their whiteboards (with 2 additional ones whose use will be apparent in time) for a gallery walk (which is when those two other boards should be completed)
I have individual sized whiteboards that I purchased a couple years back and last year we got the school to get us Home Depot boards which we had cut down to 2' x 4' size for group work.
I see one group, being given the pattern for Pascal's Triangle. (this should be a group of students who need a lower level introduction to the mathematics we will be doing). Two other groups will split up the combinations (evens one group, odds the other). Two other groups will work on binomial expansion of (x+y) with one group again doing evens and the other odds. Ideally, weaker students will get the chance to rotate from the Pascal's Triangle station to both of the other problems. Stronger students should be ok with only seeing Pascal's Triangle from in the Gallery walk.
I see the groups set up as 1. Pascal's Triangle (weaker), 2. Binomial expansion evens, 3. combinations odds, 4. binomial expansion odds, 5 combinations evens
Thoughts: I like the notion of being able to differentiate the work, with weaker students getting a view of all three procedures. I like that I'm not just showing them these things and doing a "taah-daah!" I like the idea of giving my strongest students the chance to practice distribution on a bigger problem, and have it not be busywork. I worry that I'll just get people putting (x+y)^4 = x^4 +y^4 . I'm thinking that showing the parallels for 7 rows should be sufficient and provide the students with enough practice of the skills I want. I have a germ of an idea about having students "see" the differences between permutations and combinations using differently colored beads. Maybe I can use something from that idea (which should come before this one) to flesh out the work being done by the combinations groups?
I have been trying to get the students to produce something personal to go along with these kinds of explorations (otherwise they don't remember the reason for the activity a week later) This is still something I haven't really done on this idea yet, though I'm sure I'll think of something or something will be suggested.
Saturday, July 6, 2013
Feeling terribly scattered...
I have made the decision that my next school year will be a lot like my previous couple, I will be making big changes... (the kids joke that if you have me again next year, things will be different)
I need to make the switch to a Standards Based Grading system. I know that this will allow me to more easily track where a student's deficiencies lie and hopefully inspire the students to work on specific topics on which they are struggling. I also am trying to build in a means of having students work for deeper understanding and for retention (and of topics, not the student). I will be doing this in a school where I will be the only teacher making this change, so besides having to prove the idea to my students I will also be under the watchful eyes of many others.
I need to start my class with a prescriptive assessment. We've done similar things before, but I am carefully creating a new test with certain topics in mind. My thought is that when I go to the Dr.'s that I fully expect him to run tests, make a diagnosis and then start a course of action to deal with my particular ailment(s). I certainly wouldn't want to b treated for diabetes, just because most of his patients need such treatment.
We are getting Ipads for the math department (due to a race to the top grant we were awarded by the state just before we ended our monitoring... We were a "failing" school, and managed to remove ourselves from the failing schools list... Sadly, as far as I'm aware, we're the only secondary school in the state to accomplish this). I'm sure the ipads will pose their own issues, and I do have some ideas on how to integrate them, but that will have to wait until I see if we get them immediately and how much influence we have on what apps are available to be put onto them.
I also am planning on starting to develop and use an interactive notebook system in my Algebra 2 classes. (well, the non-honors classes to start) We have our CCSS curriculum pretty much ready, I will just be creating the notebook around that format. This means the first topic my students will see in their notebooks will be Univariate Data Analysis.
To this end, I have started working on this first unit. Skipping the table of contents, grade analysis sheets, standards list (with A and B standards identified and written in student friendly language) and my expectations pages (most of which I have already created as well). My students will see a 4-door mean/median/mode/range foldable, 4 flap foldable on creating box and whisker plots, s sheet showing how to find standard deviation using a table, a page on finding measures of central tendency with the NSpire, a page on Normal Distribution and the Empirical Rule, a page on skew and z-scores. I've made homework assignments for many of these days, all with A and B problems (total of 4-6 per topic) My Normal Distribution and Empirical Rule page includes a QR link to an online Plinko simulator (this seems like a natural time to introduce the Ipads to the students). AFter these notebook days I have 2-3 data collection and analysis activities planned, one of which I know works well to discuss and illustrate Normal Distribution.
I have decided that practice with many of these topics in class will be done in pairs and/or with stations. I am half wondering if I should give a quiz to the students the day the NSpires are handed out, but before the calculator work so that I can assess how they find M/M/M/R and SD by hand, but as this is a B level standard, I don't know if its worthwhile.
I guess the questions I'm still wrestling with are: 1. how do you decide when to assess students on different standards? 2. Do you have students include practice in the interactive notebook? 3. Because its possible in my school for a student to have 3 different teachers, one each trimester, for the same course, how do I deal with students who only start to have me 2nd or 3rd trimester with regard to the INB? (I know that I will be relying heavily on the students who had me the previous trimester to help the newbies).
I snipped andstole "borrowed" heavily for some of the other pages (and some are just very simplistic) but I'll share the Standard Deviation table page. If anyone wants to see more, just let me know.
standard deviation with tables
I need to make the switch to a Standards Based Grading system. I know that this will allow me to more easily track where a student's deficiencies lie and hopefully inspire the students to work on specific topics on which they are struggling. I also am trying to build in a means of having students work for deeper understanding and for retention (and of topics, not the student). I will be doing this in a school where I will be the only teacher making this change, so besides having to prove the idea to my students I will also be under the watchful eyes of many others.
I need to start my class with a prescriptive assessment. We've done similar things before, but I am carefully creating a new test with certain topics in mind. My thought is that when I go to the Dr.'s that I fully expect him to run tests, make a diagnosis and then start a course of action to deal with my particular ailment(s). I certainly wouldn't want to b treated for diabetes, just because most of his patients need such treatment.
We are getting Ipads for the math department (due to a race to the top grant we were awarded by the state just before we ended our monitoring... We were a "failing" school, and managed to remove ourselves from the failing schools list... Sadly, as far as I'm aware, we're the only secondary school in the state to accomplish this). I'm sure the ipads will pose their own issues, and I do have some ideas on how to integrate them, but that will have to wait until I see if we get them immediately and how much influence we have on what apps are available to be put onto them.
I also am planning on starting to develop and use an interactive notebook system in my Algebra 2 classes. (well, the non-honors classes to start) We have our CCSS curriculum pretty much ready, I will just be creating the notebook around that format. This means the first topic my students will see in their notebooks will be Univariate Data Analysis.
To this end, I have started working on this first unit. Skipping the table of contents, grade analysis sheets, standards list (with A and B standards identified and written in student friendly language) and my expectations pages (most of which I have already created as well). My students will see a 4-door mean/median/mode/range foldable, 4 flap foldable on creating box and whisker plots, s sheet showing how to find standard deviation using a table, a page on finding measures of central tendency with the NSpire, a page on Normal Distribution and the Empirical Rule, a page on skew and z-scores. I've made homework assignments for many of these days, all with A and B problems (total of 4-6 per topic) My Normal Distribution and Empirical Rule page includes a QR link to an online Plinko simulator (this seems like a natural time to introduce the Ipads to the students). AFter these notebook days I have 2-3 data collection and analysis activities planned, one of which I know works well to discuss and illustrate Normal Distribution.
I have decided that practice with many of these topics in class will be done in pairs and/or with stations. I am half wondering if I should give a quiz to the students the day the NSpires are handed out, but before the calculator work so that I can assess how they find M/M/M/R and SD by hand, but as this is a B level standard, I don't know if its worthwhile.
I guess the questions I'm still wrestling with are: 1. how do you decide when to assess students on different standards? 2. Do you have students include practice in the interactive notebook? 3. Because its possible in my school for a student to have 3 different teachers, one each trimester, for the same course, how do I deal with students who only start to have me 2nd or 3rd trimester with regard to the INB? (I know that I will be relying heavily on the students who had me the previous trimester to help the newbies).
I snipped and
standard deviation with tables
Thursday, July 4, 2013
I do exit tickets wrong
I've got a good reason, really...
My class periods are 73 minutes long. How long is your attention span? Right now my mind is wandering to those biweekly staff meetings, once a month the meeting is 75 minutes and I'm rarely 100% focused on what the meeting is about. Sure I start out well, I even have a notebook each year and keep track of what we do each meeting.
I try to keep this in mind when planning a lesson, I've even been known to make the kids do the wave, get up and stretch or just find some other reason for students to do something to break up the monotony. Because of this, my 73 minutes is frequently broken into thirds or at least half. Seems like a perfect time for an exit slip.
Since I've already planned the rest of the class, I don't feel as guilty leaving a topic which just isn't sticking to reconsider and try another time. This also gives me time to go through those exit slips and if I want look at the topic again before sending my students off to their other classes. Also, if I need them to practice some part of the lesson, I now have a better idea of what they're capable of doing and what will just frustrate them. (Or the time to access and prepare a flip for them to watch at home instead of or in addition to something written).
I made up 4 (or so) different kinds of exit slips and I made a couple hundred copies of each, so the students don't necessarily know what I'm going to ask. (I tried posting links at the bottom of the post).
I realize that it's not exactly an exit slip, but there are technological tools which can accomplish something similar. At school they're pushing using the NSpire Navigator system ( not entirely because of the great cost it took to get). Sorry, TI, but I'm not a fan of the NSpires for this, because unless the kids use them almost daily that logging-in and such always takes more time than I'm willing to trade off on something like this.
I also do "my favorite no" as an opening activity a couple days a week. I've found that my exit slips from the day before frequently guide me about what to ask and whose examples to be prepared to share. I first saw the my favorite no concept in a video online, and I'm sorry to say I do not know to whom to give credit...it wasn't me, but I'll describe how I use the concept for those who don't know about it.
As students enter the room, they see MFN projected onto the board. (underneath it says, get an index card from the back holder and write one problem on the front and the other on the back, then by yourself try to solve the two problems). This gives me time to take attendance, walk around look at homework and speak to students, approx 3-6 mins. I do not have students add their names, unless I get lots of students doing nothing, in which case I have them add initials (though I see who is doing it and who isn't while walking about). I then collect the cards and sort through the 1st problem, picking out a card in which the problem was started well, but something went wrong. The class then gets to figure out what went wrong and suggest how that student could remember not to make the same mistake(s) again. While they're doing that I sort the second side to do the same thing with that side.
It works well to look at material from the previous day, but I find that it really shines for me when I need to get them thinking about prior knowledge in order to reference those skills in the lesson I am giving that day. (I recall converting 1/7 to a decimal, without a calculator, the day we started polynomial long division).
I can't see any reason to start doing exit tickets correctly... at least not as I currently use them...
exit slip #1
Exit slip #2
Exit slip #3
exit slip #4
I think there are 2 more at work... I'll try to update at some point
My class periods are 73 minutes long. How long is your attention span? Right now my mind is wandering to those biweekly staff meetings, once a month the meeting is 75 minutes and I'm rarely 100% focused on what the meeting is about. Sure I start out well, I even have a notebook each year and keep track of what we do each meeting.
I try to keep this in mind when planning a lesson, I've even been known to make the kids do the wave, get up and stretch or just find some other reason for students to do something to break up the monotony. Because of this, my 73 minutes is frequently broken into thirds or at least half. Seems like a perfect time for an exit slip.
Since I've already planned the rest of the class, I don't feel as guilty leaving a topic which just isn't sticking to reconsider and try another time. This also gives me time to go through those exit slips and if I want look at the topic again before sending my students off to their other classes. Also, if I need them to practice some part of the lesson, I now have a better idea of what they're capable of doing and what will just frustrate them. (Or the time to access and prepare a flip for them to watch at home instead of or in addition to something written).
I made up 4 (or so) different kinds of exit slips and I made a couple hundred copies of each, so the students don't necessarily know what I'm going to ask. (I tried posting links at the bottom of the post).
I realize that it's not exactly an exit slip, but there are technological tools which can accomplish something similar. At school they're pushing using the NSpire Navigator system ( not entirely because of the great cost it took to get). Sorry, TI, but I'm not a fan of the NSpires for this, because unless the kids use them almost daily that logging-in and such always takes more time than I'm willing to trade off on something like this.
I also do "my favorite no" as an opening activity a couple days a week. I've found that my exit slips from the day before frequently guide me about what to ask and whose examples to be prepared to share. I first saw the my favorite no concept in a video online, and I'm sorry to say I do not know to whom to give credit...it wasn't me, but I'll describe how I use the concept for those who don't know about it.
As students enter the room, they see MFN projected onto the board. (underneath it says, get an index card from the back holder and write one problem on the front and the other on the back, then by yourself try to solve the two problems). This gives me time to take attendance, walk around look at homework and speak to students, approx 3-6 mins. I do not have students add their names, unless I get lots of students doing nothing, in which case I have them add initials (though I see who is doing it and who isn't while walking about). I then collect the cards and sort through the 1st problem, picking out a card in which the problem was started well, but something went wrong. The class then gets to figure out what went wrong and suggest how that student could remember not to make the same mistake(s) again. While they're doing that I sort the second side to do the same thing with that side.
It works well to look at material from the previous day, but I find that it really shines for me when I need to get them thinking about prior knowledge in order to reference those skills in the lesson I am giving that day. (I recall converting 1/7 to a decimal, without a calculator, the day we started polynomial long division).
I can't see any reason to start doing exit tickets correctly... at least not as I currently use them...
exit slip #1
Exit slip #2
Exit slip #3
exit slip #4
I think there are 2 more at work... I'll try to update at some point
Monday, July 1, 2013
how fair is it?
my next blog posting was going to be about why I thought one particular unit was difficult for my students last year and what I was planning on doing about it this year. I'm sure it will be coming soon, but instead....
I had a discussion with 2 other teachers in my school. I, as a general rule, this past year wrote most of the assessments. It primarily worked out that way because I was the one teaching the honors class, so I was reaching the material first. Then, as they caught up, we would review the assessments which I had created and looking at the honor's classes results on those assessments we would "agree" to modify them. I put the "agree" in quotations because it wasn't infrequent for items to be removed, made significantly easier (reduction in Depth of Knowledge) or otherwise significantly changed.
I'm not using my, limited, platform to complain about my co-workers. My thoughts are instead drawn to the comment of one of them and I want to stream of consciousness my thoughts about that comment.
The question had the students performing a task which they had not previously done in class. It was a question relating to probability - and I wish I had saved it to post it here, but when I copied my files at the end of the year onto my portable hard-drive the original was replaced by what was given to the students instead. (If I find it, I'll try to add it, but its not really necessary for the rest of the posting)
Is it appropriate for students to be asked on an assessment to perform a task or experiment uniquely different than something they've previously seen in class, but still within the scope of the curriculum?
The math coach we had said that my question was "ambitious" but she refrained from commenting further when asked about the decision of the rest of the Algebra 2 teachers to remove the problem. It was pointed out that there were plenty of other kinds of questions which did more closely resemble the kinds of questions the students had previously seen in class which would also assess the same standard. It was further pointed out that this was a question which the honors kids had struggled with as well (I believe the percentage was about 30% had gotten it correct).
My feeling is that by only asking safe, expected kinds of problems we are limiting our students. It may be perceived as unfair, but I'd rather a spectacular attempt at a problem that was different than 10 perfectly executed examples which the students had seen, or themselves, done before. I also point out the argument I used with the other teachers before the problem was removed, - I'm sure the assessments coming down the pike will include many problems unfamiliar to my students and I want them to at least try.
I see both sides and while I feel justified in my position, I can recognize that as many of our students freeze or just write the dreaded IDK (why would they write "I Dumb Kid" on their papers anyway... I can assure you after I question a few of them each year and assure them that I seriously doubt it, they don't do it anymore in my class...lol...I also point out that they could just as easily have written IDT...I Didn't Try)
It was one thing when NY changed their standards and NY teachers felt pressured, or TX ratcheted up the testing, but now its all of us and I'd rather challenge my kids and drop the points for a question and hand out candy to the ones who succeed or fail spectacularly, rather than remove the difficult questions from the test. I want my students to know that on each test that there will be questions which they've never seen and know that something they've learned is appropriate to solving it. If individually they never have to work on something like this, then I can't imagine how they'll ever deal with the tests which are coming....
I had a discussion with 2 other teachers in my school. I, as a general rule, this past year wrote most of the assessments. It primarily worked out that way because I was the one teaching the honors class, so I was reaching the material first. Then, as they caught up, we would review the assessments which I had created and looking at the honor's classes results on those assessments we would "agree" to modify them. I put the "agree" in quotations because it wasn't infrequent for items to be removed, made significantly easier (reduction in Depth of Knowledge) or otherwise significantly changed.
I'm not using my, limited, platform to complain about my co-workers. My thoughts are instead drawn to the comment of one of them and I want to stream of consciousness my thoughts about that comment.
The question had the students performing a task which they had not previously done in class. It was a question relating to probability - and I wish I had saved it to post it here, but when I copied my files at the end of the year onto my portable hard-drive the original was replaced by what was given to the students instead. (If I find it, I'll try to add it, but its not really necessary for the rest of the posting)
Is it appropriate for students to be asked on an assessment to perform a task or experiment uniquely different than something they've previously seen in class, but still within the scope of the curriculum?
The math coach we had said that my question was "ambitious" but she refrained from commenting further when asked about the decision of the rest of the Algebra 2 teachers to remove the problem. It was pointed out that there were plenty of other kinds of questions which did more closely resemble the kinds of questions the students had previously seen in class which would also assess the same standard. It was further pointed out that this was a question which the honors kids had struggled with as well (I believe the percentage was about 30% had gotten it correct).
My feeling is that by only asking safe, expected kinds of problems we are limiting our students. It may be perceived as unfair, but I'd rather a spectacular attempt at a problem that was different than 10 perfectly executed examples which the students had seen, or themselves, done before. I also point out the argument I used with the other teachers before the problem was removed, - I'm sure the assessments coming down the pike will include many problems unfamiliar to my students and I want them to at least try.
I see both sides and while I feel justified in my position, I can recognize that as many of our students freeze or just write the dreaded IDK (why would they write "I Dumb Kid" on their papers anyway... I can assure you after I question a few of them each year and assure them that I seriously doubt it, they don't do it anymore in my class...lol...I also point out that they could just as easily have written IDT...I Didn't Try)
It was one thing when NY changed their standards and NY teachers felt pressured, or TX ratcheted up the testing, but now its all of us and I'd rather challenge my kids and drop the points for a question and hand out candy to the ones who succeed or fail spectacularly, rather than remove the difficult questions from the test. I want my students to know that on each test that there will be questions which they've never seen and know that something they've learned is appropriate to solving it. If individually they never have to work on something like this, then I can't imagine how they'll ever deal with the tests which are coming....
Saturday, June 29, 2013
Unit One Algebra 2 Univariate Data Analysis
In considering going to Standards Based Grading (SBG) I
contemplated how I would evaluate standards and realized pretty quickly that I
first had to figure out what standards I would be assessing. I have a list of goals from last year and I
am going to attempt to classify each as a P (primary) or S (secondary)
goal. My opinion is that primary goals
are ones which MUST be completed at a higher level.
Univariate Data
Analysis
Goals:
(S)
Represent data with plots on the real number line (dot plots, histograms, and
box plots).
(P)
Use statistics appropriate to the shape of the data distribution to compare
center (median, mean) and spread (interquartile range, standard deviation) of
two or more different data sets.
(S)
Recognize possible associations and trends in the data.
(S)
Interpret differences in shape, center, and spread in the context of the data
sets, accounting for possible effects of extreme data points (outliers).
(P)
Use the mean and standard deviation of a data set to fit it to a normal
distribution and to estimate population percentages.
(P)
Use calculators, spreadsheets, and tables to estimate areas under the normal
curve.
(S)
Represent data on two quantitative variables on a scatter plot, and describe
how the variables are related.
(S)
Summarize categorical data for two categories in two-way frequency tables.
(S) Interpret
relative frequencies in the context of the data (including joint, marginal, and
conditional relative frequencies).
(P)
Informally assess the fit of a function by plotting and analyzing residuals.
(S) Fit
a function to the data; use functions fitted to data to solve problems in the
context of the data. Emphasize linear, quadratic, and exponential models.
My decision on
which are primary vs secondary was based upon consideration of what kind of
questions I recall being on the assessment we created last year. Though given the rigor which Smarter
Balanced/ PAARC seems to be requiring I may decide to make some changes with
them as well.
It appears I have
identified 4 primary and 7 secondary goals for this unit. At first glance this seems to be a bigger
number than I want to assess (and reassess).
I think I will try to reduce my number of secondary goals to 2-3. Perhaps I need to re-evaluate my goals for
this unit so that some of them are more inclusive of other goals. I'm also thinking that I should translate these goals into more "kid friendly" language.
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