Well, I took all of the accumulated Challenge questions that they wrote and printed them off of Padlet. This is a built in feature of Padlet, so it is very easy to do. I made 15 copies and then had students select groups (of 2 or 3). Each group had a set (or 2) of the questions. They worked on the whiteboards or their own notebook paper and proceeded to solve them. This is where the fun really got going in the classroom as I heard students say "these are hard!" or "so-and-so, why did you have to write this problem?". Wasn't that the point. The directions said the questions had to be challenging!!
There were a few mistakes with their answer keys that we found along the way, but then I would hear "that would have been a great choice for a multiple choice wrong answer". AHA!!! They are getting it! Sometimes the author would work the problem and find a mistake before the class did and then we would make corrections to typos they had made. I enjoyed that the pressure of their peers seeing their work made them really want to take ownership and put their best work out there! One of the students had to prove that her answer was, in fact, correct and when the students saw that they had not manipulated the answer far enough, there was a big groan. Several of them were sure they had it correct and when we ALL worked it out on the board, they saw several versions of the correct answer, dependent upon where they stopped in their mathematical manipulations. It was a thing of beauty....everyone was correct!! At this level, it has taken all year to teach them that there are several versions of the correct answer, not just one answer (as they are typically taught in so many math classes). I LOVE THAT! I have frequently told them that they are master manipulators at this level.
Next year I plan to use this at the end of both semesters for final exam review. I plan to incorporate this into my other classes as well. The students love working on each other's problems and having made each one an expert in one section helped each student shine when they got to explain their topic. So glad I thought of this idea. Even happier that my friend @KathleenDiver told me about Padlet.
Thursday, April 24, 2014
Wednesday, April 23, 2014
AP Calc Review (part 1)
Previous set up: I had the tech support staff load MathType on the lab computers so students would be able to use it. I made a list of all the sections we covered in AP Calc this year and created slips with a different section number on them. In addition, I typed a master student list so they would be able to write down their assigned section and I could keep track of each students assignment. I wrote the directions for the assignment so students would have a hard copy (I would be happy to send them to you).
The requirements: were that they had to post 3 problems for their topic/section. One question had to be posted to the "Easy" page, one to the "Medium" page and one to the "Challenge" page. One of their 3 questions had to be multiple choice with good distractors. In addition, they were turning in solutions to their 3 problems on paper and solutions for their distractors being appropriate (so 3 ways to get the wrong answers provided and 1 way to get the correct answer).
Days 1 and 2: I took the students to the computer lab. The first day, I had to teach them how to create a formula using MathType inside a Word document and then how to snip it and save it so they could retrieve it. We practiced this together. Then I showed them how to access Padlet (I had created links on the school web page for my class, so they only had to open the link). Padlet is so incredibly easy to use! It did not take much explanation after that. The beauty of this was both their notes and homework pages are online for them to access, so they had the ability to check what their topic was while on the computer and then start forming their questions. The few questions that I had to answer were how to use MathType to get particular functions (exponents, infinity symbol, etc.). I didn't expect they would finish the first day, thus the reason for the second. Although unintended, there was a week between computer lab days (this had been planned to be consecutive days), but when they went back the 2nd day, they had definitely had enough time to construct the rest of their problems and multiple choices. Almost everyone finished (the couple that didn't came in before or after school or at lunch to do so).
All I had to do was check to see that every student had posted their 3 questions (one multiple choice) and arrange the topics in order by section number (for ease of student use). The second day in the lab, I simply monitored completion and started arranging the questions in order. Students got right to work. Often if they got stuck, they would ask each other for help/ideas.
Days 3 and 4: At the conclusion of Day 2, students were assigned the Easy page for homework. They had to work out everyone's question. Since they were posted by section number, it made it easy for students to go back and review that section if they got stuck/forgot how to do the problem. The next day we went over them in class (one problem at a time). I put them up on the board (using the LCD) and asked each "expert" for the correct answer to their problem. Sometimes the class was in complete agreement and we moved on, sometimes they needed to know how to arrive at that solution. At this point, I took the "expert's" work and put it under the document camera to display. The expert was then able to explain their solution. We found a few cases of the expert making their own mistake, but we didn't dwell on that, and I pointed out that I NEVER get 100's on the tests that I make and always make sure I check 5 smart students papers before I grade the entire set. This reminds the students that its okay to make mistakes (we all do).
Here's what I learned (and why I will use it again): The student's were driven to make good questions. They enjoyed being the expert and EVERY student got to be an expert on each of the Padlet pages, so each student "got a turn". They enjoyed working each other's questions. I heard students say "this was actually fun". It made it a great way to review every section by using the power of collaboration effectively. Best part: I believe that this really enlightened the students about "distractors" and how to look for them as they seek the correct answer in the multiple choice questions. They were able to spot some of the distractors right away and tell me what was wrong with that choice. I couldn't have planned that part any better!! Since they all had to create one multiple choice and their own distractors, they all experienced this.
Next up: the Challenge questions! I have a different plan for these. Can't wait to see how they impact the students thinking.
The requirements: were that they had to post 3 problems for their topic/section. One question had to be posted to the "Easy" page, one to the "Medium" page and one to the "Challenge" page. One of their 3 questions had to be multiple choice with good distractors. In addition, they were turning in solutions to their 3 problems on paper and solutions for their distractors being appropriate (so 3 ways to get the wrong answers provided and 1 way to get the correct answer).
Days 1 and 2: I took the students to the computer lab. The first day, I had to teach them how to create a formula using MathType inside a Word document and then how to snip it and save it so they could retrieve it. We practiced this together. Then I showed them how to access Padlet (I had created links on the school web page for my class, so they only had to open the link). Padlet is so incredibly easy to use! It did not take much explanation after that. The beauty of this was both their notes and homework pages are online for them to access, so they had the ability to check what their topic was while on the computer and then start forming their questions. The few questions that I had to answer were how to use MathType to get particular functions (exponents, infinity symbol, etc.). I didn't expect they would finish the first day, thus the reason for the second. Although unintended, there was a week between computer lab days (this had been planned to be consecutive days), but when they went back the 2nd day, they had definitely had enough time to construct the rest of their problems and multiple choices. Almost everyone finished (the couple that didn't came in before or after school or at lunch to do so).
All I had to do was check to see that every student had posted their 3 questions (one multiple choice) and arrange the topics in order by section number (for ease of student use). The second day in the lab, I simply monitored completion and started arranging the questions in order. Students got right to work. Often if they got stuck, they would ask each other for help/ideas.
Days 3 and 4: At the conclusion of Day 2, students were assigned the Easy page for homework. They had to work out everyone's question. Since they were posted by section number, it made it easy for students to go back and review that section if they got stuck/forgot how to do the problem. The next day we went over them in class (one problem at a time). I put them up on the board (using the LCD) and asked each "expert" for the correct answer to their problem. Sometimes the class was in complete agreement and we moved on, sometimes they needed to know how to arrive at that solution. At this point, I took the "expert's" work and put it under the document camera to display. The expert was then able to explain their solution. We found a few cases of the expert making their own mistake, but we didn't dwell on that, and I pointed out that I NEVER get 100's on the tests that I make and always make sure I check 5 smart students papers before I grade the entire set. This reminds the students that its okay to make mistakes (we all do).
Here's what I learned (and why I will use it again): The student's were driven to make good questions. They enjoyed being the expert and EVERY student got to be an expert on each of the Padlet pages, so each student "got a turn". They enjoyed working each other's questions. I heard students say "this was actually fun". It made it a great way to review every section by using the power of collaboration effectively. Best part: I believe that this really enlightened the students about "distractors" and how to look for them as they seek the correct answer in the multiple choice questions. They were able to spot some of the distractors right away and tell me what was wrong with that choice. I couldn't have planned that part any better!! Since they all had to create one multiple choice and their own distractors, they all experienced this.
Next up: the Challenge questions! I have a different plan for these. Can't wait to see how they impact the students thinking.
Thursday, April 10, 2014
Fear of Failure
A former student recommended that I read about a topic she had studied in one of her teacher preparation classes. The topic: Quality of Failure. I was immediately intrigued and google searched it only to find a couple of fascinating articles Teaching to Fail and The Freedom to Fail. I realize that students have great respect for when I wrestle with a question that they pose or if I find that the math is "not working out in class" and have to pause the class to figure it out. Some of them even enjoy wrestling with me to arrive at a solution or conclusion about "the magic" that makes the math work. I love these moments.
The challenge is getting more students on board. They have grown up in a microwave world and want the instant solutions without a lot of effort or thought, so some of them frequently just sit and wait until "the smarter people" come up with the solution or the rule for the pattern. I often have to "Ssshhhh" students and remind them not to "spoiler alert" when they want to blurt out the pattern they have spotted. I remind students to wait for others to process and develop their own hypothesis before sharing "the trick". What I hope to accomplish next year (and perhaps a little with the few remaining days this year) is to encourage students that failure is how we learn. I am always telling my students that they don't learn from the problems that they get right, only the wrong ones IF they work them again to get to the correct solution. I wish I had a dime for the number of times I have seen a student look at only the score on their test and toss it back into the graded pile. Despite the fact that I encourage them to come in for extra help so they can rework the problems, they don't. It is disappointing. I suspect my quality of failure in this respect is still low because I haven't figured out an effective way to get them to rework missed problems or focus on those failures so that they can learn from them.
I hope to incorporate some new strategies next year that will require students to stop and reflect on the problems that they get wrong, and write me an explanation as to why they missed it and then write a new question similar to the missed problem with a solution as well.
I want them to celebrate their failures because it is through those that growth and learning both happen! Looking forward to failure!!
The challenge is getting more students on board. They have grown up in a microwave world and want the instant solutions without a lot of effort or thought, so some of them frequently just sit and wait until "the smarter people" come up with the solution or the rule for the pattern. I often have to "Ssshhhh" students and remind them not to "spoiler alert" when they want to blurt out the pattern they have spotted. I remind students to wait for others to process and develop their own hypothesis before sharing "the trick". What I hope to accomplish next year (and perhaps a little with the few remaining days this year) is to encourage students that failure is how we learn. I am always telling my students that they don't learn from the problems that they get right, only the wrong ones IF they work them again to get to the correct solution. I wish I had a dime for the number of times I have seen a student look at only the score on their test and toss it back into the graded pile. Despite the fact that I encourage them to come in for extra help so they can rework the problems, they don't. It is disappointing. I suspect my quality of failure in this respect is still low because I haven't figured out an effective way to get them to rework missed problems or focus on those failures so that they can learn from them.
I hope to incorporate some new strategies next year that will require students to stop and reflect on the problems that they get wrong, and write me an explanation as to why they missed it and then write a new question similar to the missed problem with a solution as well.
I want them to celebrate their failures because it is through those that growth and learning both happen! Looking forward to failure!!
Thursday, March 27, 2014
1st official day of "flipped"!
I DID IT!! I made a video (well, it took me 3-five minute videos actually) and posted it (them) to my YouTube channel, and subsequently assigned the kids to take notes on them. (I have preprinted notes that we normally use in class, so now the students will simply fill them in at home). It took a few tries to figure out TouchCast and how to load it to the internet, but I managed. So what came next?
Let me tell you!! I spent a few hours the night before thinking through what "the next day" should look like. For now, it will have to be synchronous (baby steps), so I made an agenda on the board (so I would remember what I needed them to do in class), and composed a "good problem" for them that would check their understanding of what they had learned. That was the 2nd item on the agenda. The first was for them to answer the question: Why do we need to know the washer method? We had just finished learning the disk method and I wanted to know why we couldn't just keep using that method. Wasn't that method "good enough"? I was pleased that they had that answer ready to give me!! But then something happened that I wasn't expecting....they had their own questions. In my head I was thinking "I should have thought of that/those questions, that's a good question!" Boy, old habits (me being in control of their learning) are sure gonna die hard!! So they proceeded to ask clarifying questions and then I decided that they really needed to "get to work" and try the problems I had chosen for them to complete in class. Once again....overachiever on my part (too many questions for them to finish). It will take me awhile to cognitively accept that fewer is actually better because they are going DEEPER!! And they are DISCUSSING!! I was thrilled about that!!
However, all of a sudden I felt "lonely". No one was focusing on me!! What was I supposed to do?! Of course I knew the answer to the question already, but nevertheless, I was mentally adjusting to me not being the center of attention. I felt like Cinderella (not the princess version that goes to the ball), the servant version who has to jump on command when a group needed me to intervene because they couldn't resolve their solution without me taking sides (affirming one side was correct and the other side made a mistake) or assisting the group who had another clarifying question. I have to adjust to a new role!! The best part is that I REALLY LOVE THIS NEW ROLE!! Everyday that I am in the front explaining, the voices in my head are screaming (THEY should be DOING something other than listening to you!! THEY should be active, not passive! THEY should be discussing, not copying notes!) I want those voices to go away, and today was the day!!!
Here is the funny part: the mental shift is not just mine! The first question I heard was "was that ALL we had to do for homework..watch the video and take notes?" It really seemed "too easy" for them! But the math power that was unleashed today from their working together on those "hard problems" they have been skipping (or faking doing) on their homework was such a "rush" to feel! I can't wait to feel it more and more!
As a side note: 100% of the students in my first period watched the video and filled in their notes. Only 1 student in period 2 skipped it and two had been absent the day before when the new instructions were given. I made all 3 of them watch the videos immediately (2 on their cell phones and 1 at my computer) and as soon as their were finished, they jumped right into their groups and started working!! I don't think I will necessarily have that success rate everyday, but I was thrilled that it started off so well!!
Let me tell you!! I spent a few hours the night before thinking through what "the next day" should look like. For now, it will have to be synchronous (baby steps), so I made an agenda on the board (so I would remember what I needed them to do in class), and composed a "good problem" for them that would check their understanding of what they had learned. That was the 2nd item on the agenda. The first was for them to answer the question: Why do we need to know the washer method? We had just finished learning the disk method and I wanted to know why we couldn't just keep using that method. Wasn't that method "good enough"? I was pleased that they had that answer ready to give me!! But then something happened that I wasn't expecting....they had their own questions. In my head I was thinking "I should have thought of that/those questions, that's a good question!" Boy, old habits (me being in control of their learning) are sure gonna die hard!! So they proceeded to ask clarifying questions and then I decided that they really needed to "get to work" and try the problems I had chosen for them to complete in class. Once again....overachiever on my part (too many questions for them to finish). It will take me awhile to cognitively accept that fewer is actually better because they are going DEEPER!! And they are DISCUSSING!! I was thrilled about that!!
However, all of a sudden I felt "lonely". No one was focusing on me!! What was I supposed to do?! Of course I knew the answer to the question already, but nevertheless, I was mentally adjusting to me not being the center of attention. I felt like Cinderella (not the princess version that goes to the ball), the servant version who has to jump on command when a group needed me to intervene because they couldn't resolve their solution without me taking sides (affirming one side was correct and the other side made a mistake) or assisting the group who had another clarifying question. I have to adjust to a new role!! The best part is that I REALLY LOVE THIS NEW ROLE!! Everyday that I am in the front explaining, the voices in my head are screaming (THEY should be DOING something other than listening to you!! THEY should be active, not passive! THEY should be discussing, not copying notes!) I want those voices to go away, and today was the day!!!
Here is the funny part: the mental shift is not just mine! The first question I heard was "was that ALL we had to do for homework..watch the video and take notes?" It really seemed "too easy" for them! But the math power that was unleashed today from their working together on those "hard problems" they have been skipping (or faking doing) on their homework was such a "rush" to feel! I can't wait to feel it more and more!
As a side note: 100% of the students in my first period watched the video and filled in their notes. Only 1 student in period 2 skipped it and two had been absent the day before when the new instructions were given. I made all 3 of them watch the videos immediately (2 on their cell phones and 1 at my computer) and as soon as their were finished, they jumped right into their groups and started working!! I don't think I will necessarily have that success rate everyday, but I was thrilled that it started off so well!!
Thursday, March 13, 2014
Run Forest, Run!!
I love that I can get my students to run to class on test days. I was discussing with my students about their test tomorrow and as we were reviewing, I put 6 of the formulas (they were supposed to memorize) up on the board. I then proceeded to have them tell me what those formulas were. As expected, they can collectively tell me with no problem. However, many of them commented with "If we had only had the formulas on the group test, we would have done better." (more on the group test to follow) I then told them, "by the way, remember: if you get to class early tomorrow, you can start the test early. These formulas will be up on the board." Someone then asked, "will you leave them up there until the bell rings?" GENIUS IDEA!! I wish I had thought of it myself, but no matter, I am definitely stealing it!! So I said, "Sure!! I will erase it when the tardy bell rings." You would have thought that I had just opened up a treasure chest and everyone was able to dig in! My 6th period welcomed that news eagerly as well. Honestly, my intent had been to leave the 6 formulas up all period, but why spoil a good suggestion?! So, again tomorrow I will have my students RUNNING to class to take a test!! And, after all, it benefits them by giving them a few more minutes.
Group tests: Several years ago I was exposed to the ideas of group tests. I am so grateful for the days that we taught CPM (College Preparatory Mathematics) because of that concept. Fortunately that "gem" stayed with our school and most of us use it for every chapter. I found that group test days were one of THE MOST POWERFUL learning days. Recently one of my students said, "if it weren't for group tests, I would probably fail this class. I learn so much on group test days." Sure there are students who gain a good grade from those tests, but it is such a small percentage of their grade, that it cannot compensate for what they are able to display on individual test days. However, I have learned over the years, that there is SO MUCH POWER in the mathematical conversations that they have. I always enjoy when they get into a debate and have to use me to help guide them to a resolution. It shows that they have passion about what they are learning. That's a scored point for me! So as I have tried more collaboration in the classroom (in my preparation for flipped class), I am so enthused to hear the students comment on the value of those discussions for their own learning. This "new level" has been begging to be used the whole time. I just didn't have the technology, nor the savvy to unleash it. I am excited about letting kids converse more in math. Perhaps I will be able to make more of them fluent speakers!!
Group tests: Several years ago I was exposed to the ideas of group tests. I am so grateful for the days that we taught CPM (College Preparatory Mathematics) because of that concept. Fortunately that "gem" stayed with our school and most of us use it for every chapter. I found that group test days were one of THE MOST POWERFUL learning days. Recently one of my students said, "if it weren't for group tests, I would probably fail this class. I learn so much on group test days." Sure there are students who gain a good grade from those tests, but it is such a small percentage of their grade, that it cannot compensate for what they are able to display on individual test days. However, I have learned over the years, that there is SO MUCH POWER in the mathematical conversations that they have. I always enjoy when they get into a debate and have to use me to help guide them to a resolution. It shows that they have passion about what they are learning. That's a scored point for me! So as I have tried more collaboration in the classroom (in my preparation for flipped class), I am so enthused to hear the students comment on the value of those discussions for their own learning. This "new level" has been begging to be used the whole time. I just didn't have the technology, nor the savvy to unleash it. I am excited about letting kids converse more in math. Perhaps I will be able to make more of them fluent speakers!!
Thursday, March 6, 2014
Math Junkies
Student A: "These were easy!"
Student B: "Yeah, but it's just integration!"
Student C: "Mrs. Torres, you've turned us into math junkies!"
If the students are trying to hurt my feelings, it's definitely NOT working with those quotes! It is so exhilarating when you have students enthused to be in the classroom, excited to be working on math that is really hard. There are some days that I throw my own pencil down saying "I hate Calculus!" when really it's a love-hate relationship with this math level that is definitely more challenging than any level I have taught before. Its been almost 30 years since I did any Calc! So my experiences are much like my students right now (only I'm a week ahead of them). LOTS of practice is required, and I understand completely how they are feeling....so MANY formulas to memorize (and they keep falling out of my head too). So we look for similarities and differences together to help each other find devices for remembering them. Songs frequently work...dances help too!! Acting out might be even better. But whatever it is that we come up with, it's so much better if they create it. After all, it's for them, not me!! Those sparks don't come "on demand". You can't pull up the on demand channel and expect to find them there. Creativity takes time, but in the end, it's worth it because they remember! Now, let's add the apply. "Experience required, apply within."
Student B: "Yeah, but it's just integration!"
Student C: "Mrs. Torres, you've turned us into math junkies!"
If the students are trying to hurt my feelings, it's definitely NOT working with those quotes! It is so exhilarating when you have students enthused to be in the classroom, excited to be working on math that is really hard. There are some days that I throw my own pencil down saying "I hate Calculus!" when really it's a love-hate relationship with this math level that is definitely more challenging than any level I have taught before. Its been almost 30 years since I did any Calc! So my experiences are much like my students right now (only I'm a week ahead of them). LOTS of practice is required, and I understand completely how they are feeling....so MANY formulas to memorize (and they keep falling out of my head too). So we look for similarities and differences together to help each other find devices for remembering them. Songs frequently work...dances help too!! Acting out might be even better. But whatever it is that we come up with, it's so much better if they create it. After all, it's for them, not me!! Those sparks don't come "on demand". You can't pull up the on demand channel and expect to find them there. Creativity takes time, but in the end, it's worth it because they remember! Now, let's add the apply. "Experience required, apply within."
Saturday, March 1, 2014
Euphoria and Barbiturates
I am aware of the disagreement in my title. But having now ventured into the world of wanting to make change for students, and after spending countless hours reflecting on what others have done (reading blogs and following pioneers on the twitter) and going to conferences for technology, I have found that it has truly rejuvenated my thoughts about my teaching! I feel SO ALIVE! I don't have enough hours in the day to learn more or try more! Sometimes when I talk with others, I find myself talking so fast because my thoughts are racing much faster than the words can exit my mouth! I think it safe to say that I have "big gulped the punch!" And this state of euphoria seems endless, and I hope it really is!!
Enter "Debbie Downers". You know what I'm talking about: the barbiturates that we sometimes work with. They are usually easy to spot in the teacher's lounge because they are there spilling their depressant drug on everyone. My mind wonders how they roll out of bed everyday and force themselves to go to work. Even more mind boggling is how they think they don't need to make any changes in what they do with students! And, that if they "buck the system enough", it will bend to meet THEIR needs (no change). It's impossible to go through a week without their "vibe" falling on you in some way.
I'm so grateful for the professional learning network, OF POSITIVITY, that twitter gives me. Thank you twitter educators for being my fountain of never ending punch!! Without you, I fear I would give into the barbiturates. Thank you district colleagues who go to Saturday trainings, without pay, because you want to be able to offer your students something more. You inspire me to do bigger and better things too! When my husband, who is not an educator, can spy on my twitter channels and comment "that is so positive", I know that I have found the "fountain of youth!".
Enter "Debbie Downers". You know what I'm talking about: the barbiturates that we sometimes work with. They are usually easy to spot in the teacher's lounge because they are there spilling their depressant drug on everyone. My mind wonders how they roll out of bed everyday and force themselves to go to work. Even more mind boggling is how they think they don't need to make any changes in what they do with students! And, that if they "buck the system enough", it will bend to meet THEIR needs (no change). It's impossible to go through a week without their "vibe" falling on you in some way.
I'm so grateful for the professional learning network, OF POSITIVITY, that twitter gives me. Thank you twitter educators for being my fountain of never ending punch!! Without you, I fear I would give into the barbiturates. Thank you district colleagues who go to Saturday trainings, without pay, because you want to be able to offer your students something more. You inspire me to do bigger and better things too! When my husband, who is not an educator, can spy on my twitter channels and comment "that is so positive", I know that I have found the "fountain of youth!".
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