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One of the best algebra texts there is: Hall and Knight's "Higher Algebra". Free e-book: http://t.co/dfMa7N6K. #math #mathchat
Saturday, March 31, 2012
Things I've Tagged (weekly)
Wednesday, March 28, 2012
Speaking of Foldables...
I've seen some discussion lately on twitter about making foldables to help summarize/review topics. As I was trying to figure out what I wanted to do in Algebra 1 on Friday (we're finishing up solving quadratic equations), I found a worksheet on my computer that was divided into three columns. One column was dedicated to solving by square roots, one was for factoring, and the third was using the quadratic formula. I decided to spice it up a bit...
What do you think?
(We started talking about quadratic equations by doing an activity with this site (a geogebra angry birds applet). Ever since then I've been using the Angry Birds font to spice things up.)
What do you think?
(We started talking about quadratic equations by doing an activity with this site (a geogebra angry birds applet). Ever since then I've been using the Angry Birds font to spice things up.)
Saturday, March 24, 2012
New ideas!
My day Friday was filled with activities I *never* would have even thought of in the past.
This was my lesson plan for precalc:
.JPG)
1. #trigis - I asked the kids to write a tweet with their "definition" of trig. They were limited to 140 characters (7 of which were taken up by the hastag #trigis). It was fun to see them thinking and editing. Someone likened it to writing a poem (he had to get kind of fancy with his words to try and condense them). I made them count their characters to ensure they had fewer than 140. I'm compiling them into a powerpoint (I know, I know) and will show them the results once they're all done.
2. Infinity Elephants - We're starting a new unit on Monday about sequences and series. It'll be a nice change (they're all "trigged" out). To get them thinking a little bit I showed Vi Hart's video Infinity Elephants. It's always interesting to see what she can do.
3. How many tesserae? (Not the right word, but they got the idea). @calcdave wrote a post on his blog about a sum that appears in the first chapter of a new movie/book series that all the kids are talking about... something called The Hunger Games. (Which I devoured as books and am excited to go see tomorrow afternoon with my book club!) I gave the kids a copy of the excerpt with the sums blanked out (it was where they were talking about how many entries Katniss and Gale had in the drawing). The kids had fun figuring that one out!
4. Create a sequence. I found a task online where students were to pick 2 numbers between 0 and 1 then create a sequence using multiplication and addition. Then we had a nice conversation about the results... depending on the numbers that were chosen, the terms approached a different value.
In Algebra 1:
I didn't have much of a plan. I'd been out on Thursday and hadn't planned ahead well. After we'd gone over some problems (that we hadn't had a chance to talk about previously because of my absence) I had all the kids get a small dry-erase whiteboard to figure out some multiple choice questions. Then we went to PollEverywhere and they submitted their answers. They loved the idea of being able to text (legally) in class! I haven't played with it much lately, but apparently you can now use images and some math type in PollEverywhere, so it might be something to check out!
In Algebra 2:
The kids had taken a test on Thursday and we're getting ready to start a unit on Exponential Functions. Seeing as how it was Friday, had been warm all week, 7th period, and several kids were missing because of a choir trip to Chicago, I didn't want to really start something new. I ended up buying a couple of those big bags of M&Ms and they worked through an exponential growth and decay activity using the candy. It was fun! I have one girl in class who is allergic to peanuts, so I was happy to see that she was in choir and I wouldn't have to come up with a work-around. They did an exponential regression on their calculators (a new skill for them, but I found some good directions and no one had any issues) so we'll be able to compare equations on Monday. The goal is to lead them to what each of the values in the equation represents, and I'm pretty sure we'll get there!
This was my lesson plan for precalc:
.JPG)
1. #trigis - I asked the kids to write a tweet with their "definition" of trig. They were limited to 140 characters (7 of which were taken up by the hastag #trigis). It was fun to see them thinking and editing. Someone likened it to writing a poem (he had to get kind of fancy with his words to try and condense them). I made them count their characters to ensure they had fewer than 140. I'm compiling them into a powerpoint (I know, I know) and will show them the results once they're all done.2. Infinity Elephants - We're starting a new unit on Monday about sequences and series. It'll be a nice change (they're all "trigged" out). To get them thinking a little bit I showed Vi Hart's video Infinity Elephants. It's always interesting to see what she can do.
3. How many tesserae? (Not the right word, but they got the idea). @calcdave wrote a post on his blog about a sum that appears in the first chapter of a new movie/book series that all the kids are talking about... something called The Hunger Games. (Which I devoured as books and am excited to go see tomorrow afternoon with my book club!) I gave the kids a copy of the excerpt with the sums blanked out (it was where they were talking about how many entries Katniss and Gale had in the drawing). The kids had fun figuring that one out!
4. Create a sequence. I found a task online where students were to pick 2 numbers between 0 and 1 then create a sequence using multiplication and addition. Then we had a nice conversation about the results... depending on the numbers that were chosen, the terms approached a different value.
In Algebra 1:
I didn't have much of a plan. I'd been out on Thursday and hadn't planned ahead well. After we'd gone over some problems (that we hadn't had a chance to talk about previously because of my absence) I had all the kids get a small dry-erase whiteboard to figure out some multiple choice questions. Then we went to PollEverywhere and they submitted their answers. They loved the idea of being able to text (legally) in class! I haven't played with it much lately, but apparently you can now use images and some math type in PollEverywhere, so it might be something to check out!
In Algebra 2:
The kids had taken a test on Thursday and we're getting ready to start a unit on Exponential Functions. Seeing as how it was Friday, had been warm all week, 7th period, and several kids were missing because of a choir trip to Chicago, I didn't want to really start something new. I ended up buying a couple of those big bags of M&Ms and they worked through an exponential growth and decay activity using the candy. It was fun! I have one girl in class who is allergic to peanuts, so I was happy to see that she was in choir and I wouldn't have to come up with a work-around. They did an exponential regression on their calculators (a new skill for them, but I found some good directions and no one had any issues) so we'll be able to compare equations on Monday. The goal is to lead them to what each of the values in the equation represents, and I'm pretty sure we'll get there!
Saturday, March 17, 2012
Things I've Tagged (weekly)
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Till Math Do Us Part - NYTimes.com
Predict length of celebrity marriages RT @pranjalbor http://t.co/i6EKrbM2 #realmath
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Patterns of Visual Math - Fractals in Nature
Naturally Occurring Fractals, Math Fractals via http://t.co/xFIhJITQ #mathed #mathchat
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http://illuminations.nctm.org/Lessons/9-12/egglaunch/egglaunch-AS-Sheet1.pdf
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http://illustrativemathematics.org/
The Illustrative Mathematics Project will provide guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards, and by publishing other tools that support implementation of the standards.
Wednesday, March 14, 2012
Sunday, March 11, 2012
Reconfiguring.
I'm amazed at the response I've gotten from my last two posts (and that doesn't count my weekly list of diigo tags). Up until a couple of weeks ago the CCSS was something that was being thrown at us for implementation in a few years. I hadn't thought about how it could change the classroom now. I realize that for some people it isn't like that - I just read yesterday where someone was changing their Algebra 2 topics to align with CCSS next year. In my district we're easing it in slowly as to hopefully avoid making holes for kids.
After my two days spent looking at the Practices, though, I realize that I can do a lot more in class to help kids prepare than just teach the "right" topics. So my plan is to focus that way a little more. I want to continue to look for "rich" problems, be less helpful, and encourage the kids to struggle with an idea instead of swooping in to bail them out.
I think I'm going to add a tab to the top of the blog just for the CCSS resources I find. That will help me (and whoever would like to read them) keep up to date with what I've found. (Do you ever look back through your downloads or tags and think, "I wish I would've known that I had that a week ago?" That's me.)
To get me started (and what got me thinking about doing that), I just saw this neat link on twitter. It's a list of web 2.0 tools aligned with some of the CCSS standards from Herkimer Central School District in Herkimer, NY. I just glanced through it, but it looks like something to definitely come back to! (Click on AM or PM session.)
Saturday, March 10, 2012
Things I've Tagged (weekly)
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Equation solving roulette - Resources - TES
Resource Shout-Out: Equation Roulette from @studymaths. Spin that wheel! http://t.co/ULRo9I3i thanks for sharing :-) #mathchat #algebra
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Are you ready for Pi Day next week (3-14)? If not
Are you ready for Pi Day next week (3-14)? If not, check out our Pinterest board for ideas: http://t.co/OhGAemNc #math via @ETACuisenaire
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Ohio Resource Center > Promise > Math > Maximizing Profits on Donut Sales
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Trigonometry: The illustrations represent a part
Trigonometry: The illustrations represent a part from the curriculum from each book: trigonometry ( http://t.co/9FGv7j8D
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The Sound of Trigonometry via http://t.co/xOAnPXNG #mathed #mathchat
Friday, March 9, 2012
Being Less Helpful.
One of the big ideas that we dealt with at the Common Core Mathematical Processes seminar was the idea of giving students "rich" problems that they can interpret, struggle through, solve, check and then resolve if necessary. But hand-in-hand with that idea is the thought that you're not standing over them holding their hand. Students need to be able to use their resources (book, notes, neighbor, etc.) to try and think through problems on their own before asking for help.
But that's so hard.... both for them and me.
I've "trained" my Algebra 2 kids to do the opposite. If they see something they don't get right away, they raise their hand to ask how to do it. Me, in my search to be helpful, run over to them to try and clear up any misconceptions. Half of the kids either haven't even read the problem yet or have and think that they don't know how to do it. I literally run around the room like a chicken with my head cut off trying to get all of their questions answered. Never mind the fact that they have notes with example problems, a book with example problems, and people sitting next to them that might have a clue.
On Tuesday that all stopped.
I warned them. After we'd gone over some homework problems and I passed out the assignment, I told them that I'd screwed up. I'd taken away their responsibility to actually think on their own and given them an "out". This was doing them a disservice and removed from them their obligation to think about a problem before automatically raising their hands. I told them that if they got stuck, I wanted them to do a few things.
1. Read the problem.
2. If they didn't know what to do, take a moment and think about it.
3. If they still didn't know what to do, check their notes and try and find a similar problem.
4. If they couldn't find one in their notes, do the same thing in their book.
5. If they couldn't find one in their book, check with a neighbor.
6. Last resort: ask me.
As you can expect, they weren't all that happy about what I'd told them. (Somewhat) surprisingly, though, a couple of the kids spoke up and said they understood. That helped some of the resistors, but there was still some grumbling.
Did that end all questions? Did the kids start thinking on their own? Well, you know. It's going to take time. My plan is to stick to my guns and continue to encourage them to struggle. (Note to self: re-read this post on August 21st next year!) I've created some monsters and that won't change over night. But they're starting to use their notes and each other as resources to help solve problems.
The amount of homework that had been completed the next day was much lower than normal.... kids had given up when they hit a rough spot. I'm hoping that if I'm consistent with my actions they'll realize that it's not going to change and they're going to have to step it up.
I'm hoping.
But that's so hard.... both for them and me.
I've "trained" my Algebra 2 kids to do the opposite. If they see something they don't get right away, they raise their hand to ask how to do it. Me, in my search to be helpful, run over to them to try and clear up any misconceptions. Half of the kids either haven't even read the problem yet or have and think that they don't know how to do it. I literally run around the room like a chicken with my head cut off trying to get all of their questions answered. Never mind the fact that they have notes with example problems, a book with example problems, and people sitting next to them that might have a clue.
On Tuesday that all stopped.
I warned them. After we'd gone over some homework problems and I passed out the assignment, I told them that I'd screwed up. I'd taken away their responsibility to actually think on their own and given them an "out". This was doing them a disservice and removed from them their obligation to think about a problem before automatically raising their hands. I told them that if they got stuck, I wanted them to do a few things.
1. Read the problem.
2. If they didn't know what to do, take a moment and think about it.
3. If they still didn't know what to do, check their notes and try and find a similar problem.
4. If they couldn't find one in their notes, do the same thing in their book.
5. If they couldn't find one in their book, check with a neighbor.
6. Last resort: ask me.
As you can expect, they weren't all that happy about what I'd told them. (Somewhat) surprisingly, though, a couple of the kids spoke up and said they understood. That helped some of the resistors, but there was still some grumbling.
Did that end all questions? Did the kids start thinking on their own? Well, you know. It's going to take time. My plan is to stick to my guns and continue to encourage them to struggle. (Note to self: re-read this post on August 21st next year!) I've created some monsters and that won't change over night. But they're starting to use their notes and each other as resources to help solve problems.
The amount of homework that had been completed the next day was much lower than normal.... kids had given up when they hit a rough spot. I'm hoping that if I'm consistent with my actions they'll realize that it's not going to change and they're going to have to step it up.
I'm hoping.
Tuesday, March 6, 2012
Common Core Mathematical Practices
I spent two days last week at a conference led by our county ESC entitled Focusing on the Mathematical Practices of the Common Core Grades 9 - 12. Honestly, a lot of the reason I try to go to different seminars is just to get out of the building and shake up my schedule a bit. It's hard to prepare for 2 days of a substitute, but changing the routine is sometimes worth it.
I was surprised by how much I enjoyed my two days. Instead of focusing on what's going where in our classes, we talked a lot about how to focus our instruction. There are 8 standards for Mathematical Practice that I feel like I know inside and out.
1. Make sense of problems and persevere in solving them. Perseverance was a big issue that we talked about. If you have students who will keep trying when they feel like they don't know how to do a problem, then I salute you. Most of mine won't. I get so tired of seeing blanks after kids have "done" their homework... or big ?s. (Know what I mean?)
2. Reason abstractly and quantitatively. Important here was the ability to decontextualize (make a problem more abstract) and contextualize (apply the numbers at hand). Tough for a lot of kids.
3. Construct viable arguments and critique the reasoning of others. Although it doesn't have to be a formal/written down process, I've started having the kids "check" the work of their classmates (they just accuse me of being lazy and making them do it). It's amazing how much they learn by going through a problem to try and find something wrong.
4. Model with mathematics. The kicker to us on this practice was the last line: "They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served it's purpose." What?! Check your work? Make sure it makes sense? And if it doesn't make sense, try to fix it?! Blasphemy. And you'd think I was torturing students in asking them to do that. Darin Hausberger, (@dhausberger) had a quote that I liked: "You may have an answer, but is it a solution?"
5. Use appropriate tools strategically. Don't automatically reach for the calculator (as we were reminded, paper and pencil are tools too!). But if there's a calculation that you can't do, go for it. Or if there's something online that you need to use, do that too.
6. Attend to precision. I originally saw this as more of a "watch your rounding" type deal. But it turns out that the premise is that students need to make sure to label axes, units, and use the equal sign "consistently and appropriately".
7. Look for and make use of structure. My big take-away on this one was the use of scaffolding. In Algebra 1 we do a lot of solving equations in the beginning of the year. I preach "show your steps" so that they get in the habit of knowing what they're doing to solve. Now, though, we're solving quadratics by factoring, and showing how to solve 2x - 1 = 0 is something they should be able to do without all of the steps. Those who are able to do that do. Those who need a little extra time are still writing it down.
8. Look for and express regularity in repeated reasoning. Once you understand something it's ok to use patterns and shortcuts. But I wouldn't suggest teaching that from the beginning. (#7 and #8 seemed very similar in nature)
So that's my 2 days in a nutshell. We talked a lot about giving "rich" problems (ala Dan Meyer, who was mentioned quite often), giving guidance but not answers, and the general idea of "Be Less Helpful".
It was a good 2 days; I brought away a lot.
HCESC (who led the program) has set up a blog and will be updating with different resources. Check it out.
One last thing - we were all given a ring of cards with questions meant to help you guide students in class. Looks like it has some good ideas on it. The questions were included in the appendix of a manual that we received... if you're interested in a copy let me know - I'll try and scan my manual and email 'em out.
(They probably won't be pretty colors like mine, but you can deal with that.)
**Please email me if you'd like a copy! KFouss @ gmail . com
I was surprised by how much I enjoyed my two days. Instead of focusing on what's going where in our classes, we talked a lot about how to focus our instruction. There are 8 standards for Mathematical Practice that I feel like I know inside and out.
1. Make sense of problems and persevere in solving them. Perseverance was a big issue that we talked about. If you have students who will keep trying when they feel like they don't know how to do a problem, then I salute you. Most of mine won't. I get so tired of seeing blanks after kids have "done" their homework... or big ?s. (Know what I mean?)
2. Reason abstractly and quantitatively. Important here was the ability to decontextualize (make a problem more abstract) and contextualize (apply the numbers at hand). Tough for a lot of kids.
3. Construct viable arguments and critique the reasoning of others. Although it doesn't have to be a formal/written down process, I've started having the kids "check" the work of their classmates (they just accuse me of being lazy and making them do it). It's amazing how much they learn by going through a problem to try and find something wrong.
4. Model with mathematics. The kicker to us on this practice was the last line: "They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served it's purpose." What?! Check your work? Make sure it makes sense? And if it doesn't make sense, try to fix it?! Blasphemy. And you'd think I was torturing students in asking them to do that. Darin Hausberger, (@dhausberger) had a quote that I liked: "You may have an answer, but is it a solution?"
5. Use appropriate tools strategically. Don't automatically reach for the calculator (as we were reminded, paper and pencil are tools too!). But if there's a calculation that you can't do, go for it. Or if there's something online that you need to use, do that too.
6. Attend to precision. I originally saw this as more of a "watch your rounding" type deal. But it turns out that the premise is that students need to make sure to label axes, units, and use the equal sign "consistently and appropriately".
7. Look for and make use of structure. My big take-away on this one was the use of scaffolding. In Algebra 1 we do a lot of solving equations in the beginning of the year. I preach "show your steps" so that they get in the habit of knowing what they're doing to solve. Now, though, we're solving quadratics by factoring, and showing how to solve 2x - 1 = 0 is something they should be able to do without all of the steps. Those who are able to do that do. Those who need a little extra time are still writing it down.
8. Look for and express regularity in repeated reasoning. Once you understand something it's ok to use patterns and shortcuts. But I wouldn't suggest teaching that from the beginning. (#7 and #8 seemed very similar in nature)
So that's my 2 days in a nutshell. We talked a lot about giving "rich" problems (ala Dan Meyer, who was mentioned quite often), giving guidance but not answers, and the general idea of "Be Less Helpful".
It was a good 2 days; I brought away a lot.
HCESC (who led the program) has set up a blog and will be updating with different resources. Check it out.
(They probably won't be pretty colors like mine, but you can deal with that.)
**Please email me if you'd like a copy! KFouss @ gmail . com
Saturday, March 3, 2012
Things I've Tagged (weekly)
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http://teachers.henrico.k12.va.us/math/HCPSAlgebra1/Documents/8-4/FactoringOldPolyGame.pdf
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GeoGebra Tutorial 11 – Sliders and Graphs of Trigonometric FunctionsMathematics and Multimedia
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10 Seriously Cool Careers That Need Maths Maths Tips From Maths Insider
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Free Technology for Teachers: The History of Calendars, Leap Year, and Daylight Savings
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Burst Resistant Fitball with Feet - Fast & Free Shipping - Therapy Balls
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How Sitting on a Ball Helps Kids Focus and Do Better In School | Gaiam Life
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Free Technology for Teachers: More GeoGebra Tutorials for Beginners
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