I'm going to start out by saying my students write to learn with every quiz or test and every homework assignment without knowing it. With every quiz and test they have to make corrections and explain why they missed what they missed or how they know the new answer is correct. They were given the expectation that they will complete corrections this way, or they would not get credit. Just an answer with no explanation does not get them credit. My Pre-Calculus students are better at explaining themselves than my Advanced Functions students. Sometimes the AFM kids try to get away with "I forgot how to do it." or "I plugged it in the calculator wrong."
In Pre-Calculus we are learning about Vectors. This Physics related topic always has at least one question on the NC Final Exam but with Fridays gone and the personalities of our lovely juniors, it's going to be a struggle to get through this in the time allotted. Vectors have many fun applications and there are many different things that can be done with them. The past 2 days, we've done Vector Stations. One station, they were a human vector. They had to walk the path of a vector, draw it out on their paper, then discuss if the order in which they followed the directions mattered. In another station, they had to follow directions in order to find "treasure" on a pirate treasure map. In another station, they had to solve some word problems that dealt with airplanes and wind and swimming with water currents. In the last station, they watched a video dealing with vectors in the NFL and read an article with some applications. In this station, they filled out the chart in this packet while they watched the video. Then, they read the article and made comments (the directions were "If you think it, write it. Even if it's "Oh! That's pretty cool."). They switched papers and made comments on their comments (like we did in our PD). Some students did really well, while other students were saying things like "I didn't know what to write." or "I didn't think anything about this." My response was "Did you really read it and try?"
I think it's still hard for students to understand why there is writing and even reading in a math class. I just had to get up to explain something they could have found out by reading the directions. They've had that problem a lot lately. That and "I don't know how to do this." Okay, well have you even thought about it? No. Hmmm...
I'll admit, the article didn't have a lot of content in it, so maybe they didn't think a whole lot about it. Even when I read the article and even the book, I don't have a lot of comments to make. I can definitely relate with them in that they don't like to read in math. This group also thinks way too much into things. I was just asked "What do you mean make a comment on their comment?" I mean exactly what I said. There's constantly heated "academic discussions" on who is correct in solving the problem. It usually ends up in they're both right.. they're just not listening to one another and fully understanding one another. Sometimes they're too smart for their own good.....
Thursday, October 30, 2014
Monday, October 13, 2014
Save the Last Word Activity - Interpreting Data
I gave a CFA on constructing and analyzing graphs to display data. An overwhelming majority demonstrated that they could calculate statistics and construct graphs given a data set; however, several seemed to struggle when they were asked to use graphs (primarily box and whisker plots) to compare and interpret data. Through questioning, I found that most could recall that a box and whisker plot split data into 4 sections, but could not use that to form sentences about a set of data (For example: At least 75% scored a 75 or higher on their test). I thought the "Save the Last Word" activity would benefit students who were struggling by letting them get input from their peers to help them create better sentences to describe data rather than by simply saying "The median is..."
Here's how I framed the activity:
For their warm up, a set of two box and whisker plots comparing sale prices for two stores were displayed. Students were given approximately 5 minutes to write down anything they could read from those plots with regards to determining which store was the "better" buy.
At the end of the 5 minutes, I put the instructions for "Save the Last Word" on the board. Students were already sitting in groups of 4, so I kept them in these groups. Each group numbered off 1-4 so that I could identify who was speaking at which times.
We then went through a round where Person 1 would state one of their findings from the box and whisker plots. Then, the rest of the group had 1 minute to respond to the initial person's finding. After the group responded, the original person could keep their sentence the same, or could edit their statement based on what the group said.
We went around until everyone had the chance to make one statement and receive as response from their group.
At the end of the activity, I asked every one to write down something new that they learned about box and whisker plots or data in the activity. I was pleased to see that the majority of the class felt they learned something.
Reflection:
"Silent Time": My freshmen are really going to need some "training" on what is expected during silence. Their instinct is to respond immediately. When a student or group did not have much to say, they had a tendency to want to start discussing anything and everything. It took a couple of stern looks and re-directions to guide groups to participate in accordance with the guidelines.
Did they learn?: I was happy to see that most had something they felt they took away from the activity. Some learned "new" things like the fact that a box and whisker plot divides data into 4 sections (I know, we had already discussed this!). Others stated that they had a better understanding/visualization of what it meant to split data into 4 sections and how to use that to interpret two graphs.
What Now: For the first time, the activity was awkward. The students wanted to talk, I wanted them to be quiet. Why weren't they using this time to think??? But, in retrospect, I should have expected awkwardness. Students are often expected to respond immediately so it is going to take some getting used to for them and me. In the future, I want to provide a little more structure for what is expected during the quiet time. If there is time left over, students should write down comments and questions so that they have more to discuss in the "group discussion" time. It is definitely going to take some practice, but I look forward to trying the activity again!
Here's how I framed the activity:
For their warm up, a set of two box and whisker plots comparing sale prices for two stores were displayed. Students were given approximately 5 minutes to write down anything they could read from those plots with regards to determining which store was the "better" buy.
At the end of the 5 minutes, I put the instructions for "Save the Last Word" on the board. Students were already sitting in groups of 4, so I kept them in these groups. Each group numbered off 1-4 so that I could identify who was speaking at which times.
We then went through a round where Person 1 would state one of their findings from the box and whisker plots. Then, the rest of the group had 1 minute to respond to the initial person's finding. After the group responded, the original person could keep their sentence the same, or could edit their statement based on what the group said.
We went around until everyone had the chance to make one statement and receive as response from their group.
At the end of the activity, I asked every one to write down something new that they learned about box and whisker plots or data in the activity. I was pleased to see that the majority of the class felt they learned something.
Reflection:
"Silent Time": My freshmen are really going to need some "training" on what is expected during silence. Their instinct is to respond immediately. When a student or group did not have much to say, they had a tendency to want to start discussing anything and everything. It took a couple of stern looks and re-directions to guide groups to participate in accordance with the guidelines.
Did they learn?: I was happy to see that most had something they felt they took away from the activity. Some learned "new" things like the fact that a box and whisker plot divides data into 4 sections (I know, we had already discussed this!). Others stated that they had a better understanding/visualization of what it meant to split data into 4 sections and how to use that to interpret two graphs.
What Now: For the first time, the activity was awkward. The students wanted to talk, I wanted them to be quiet. Why weren't they using this time to think??? But, in retrospect, I should have expected awkwardness. Students are often expected to respond immediately so it is going to take some getting used to for them and me. In the future, I want to provide a little more structure for what is expected during the quiet time. If there is time left over, students should write down comments and questions so that they have more to discuss in the "group discussion" time. It is definitely going to take some practice, but I look forward to trying the activity again!
Tuesday, October 7, 2014
Silence is Hard
Today, I began my unit on cyberbullying. Rather than continue the way I have taught it before, I decided to have students watch a video on a news report about cyberbullying, and read 1 of 2 articles. I chose two different articles in order to differentiate for reading levels.
Resources: (hyperlinked)
News Article Video
Article #1
Article #2
Questions posted around room for carousel
PPT w/Directions for Group Work
We first watched the news clip about two girls being charged with involvement in a bullying case that resulted in suicide. Before allowing discussion, I then gave students their articles and explained how I wanted them to annotate, leaving the directions on the board. I set a timer for 5 minutes. That was not enough time, so I added another 5. A few students (my stronger readers) were finished within the first 5 minutes, but I wanted to give enough time for everyone to annotate fully.
I will allot 10-15 minutes for the articles in the future in order to encourage students to stay focused and help with timed reading training for final exams. (4th block had the most difficulty staying quiet after completing their initial reading.)
Students had to remain silent after completing their annotations which was easy for most of them in 3rd block. 4th block however had some issues. Although, some will have to remember not to write or play with materials while listening to others speak. The most trouble I had came from the sophomores in room 123 because they don't know how to not act like idiots when no one is watching them.
In the future, I will add to the instructions for the members to direct the rest of the group to the passage before reading in order to help those who need to read the section for better comprehension. I will also direct group members to be thinking about what their response will be when it is time for their discussion during the rest of the minute from the original speaker.
3rd block: I had students get out their phones and set a timer for 1 minute. That person was then in charge of resetting the timer for each speaker.
4th block: I tried to have students keep a timer. They could not handle this, so I had to be the one to maintain the timer for other member responses.
For the original member to respond, I will set a class timer in order to keep better timing on the group as a whole. I kept the timer hidden so students would not stare down the clock. I noticed many students stopped speaking way before the timer ran out. I was surprised that my big talkers and those who dominate the conversations definitely did not utilize a lot of their time.
3rd block: When having to sit in silence for the rest of the minute during response time, students were really good about monitoring the other students for speaking when they weren't supposed to. Overall, students discussed the material in a mature manner without much intervention from me on maintaining a respectful mien.
4th block: Had issues following directions in allowing only 1 person to speak at a time and waiting in silence. I had to stop and explain twice what I meant by not talking unless you were the person assigned to speak.
Silence is hard.
4th block: I had to have students clear their desks because they wanted to play with papers, read books, move notebooks around, just do anything else besides sit still and think. After repeatedly explaining that they just had to sit and listen, I still had some students trying to mime to one another, play with scarves, and write notes. There were a few girls that had some serious attitude issues and could not handle the silence.
Generally, 4th block finished with at least 1/2 the time left for each discussion piece, whether it was 1 minute or 2 minutes. 3rd block generally used more time for their discussions.
I love that each student was able to get a chance to respond without anyone else interfering their moment. This also gave students time to consider their responses without pressure from more vocal and outspoken students.
There were a few students I noticed that did not pay particular attention when other people were speaking. Coincidentally, these are also my lowest students.
My 3rd block had some issues reestablishing their focus with lunch interrupting their discussions. It took some time getting back on track. Students were writing notes on paper to each other, among other things, and I had to redirect their attentions.
Consistently, students used only 1 of the 2 minute response times that they were allowed in order to respond to others' points and explain why they chose their particular passages.
Because I ran out of time 3rd period and could not do the Gallery Walk, I decided to take the comments down and assign numbers for each question. I am going to give each group a question and the corresponding post it notes and have the students organize and share their findings in class.
____________________________________________________________________________
After the silent group work, I asked for students' feedback. Some feelings were (and these come from my outspoken students, the ones who always raise their hands and want to speak):
Cons:
"It's too hard to remain focused when it's so quiet."
"It's easier to think when everyone is talking."
"I didn't have enough time to give my opinion."
"It's hard to wait and remember my ideas when someone else is speaking."
"I couldn't congratulate someone when they had a good idea."
"Couldn't respond immediately to another person's thoughts."
"Silent time felt awkward."
"Didn't get to have a class discussion. Made it boring not involving the whole class."
"If you did agree and have the same answer, not much to add."
"Repeated same answers in small group so ran out of things to say."
"Got fidgety during silence."
"Misunderstandings and couldn't fix it until it was your turn to speak again."
Pros:
"It gives everyone a chance to speak without being interrupted."
"Learned how to listen to others."
"Able to hear how other people felt on the subject."
"Learned what other people are thinking and compared to your thoughts. See different opinions/mind sets."
"Kept on task w/specified times."
"Able to share your thoughts w/out fear of judgment."
____________________________________________________________________________
Side note: My 4th block came in and said my 3rd block felt as if the discussion activity was so boring they wanted to sleep. Coincidentally, students are afraid of silence and having to speak their opinions. Additionally, I want to use a chart to diagram length of responses from students to record general response times and compare them to whole group discussions.
I will also assign a "talk monitor" to help dissuade others from speaking during silent moments.
I definitely got frustrated with the students during this activity.
Post-It notes do not stick to the walls.
Resources: (hyperlinked)
News Article Video
Article #1
Article #2
Questions posted around room for carousel
PPT w/Directions for Group Work
We first watched the news clip about two girls being charged with involvement in a bullying case that resulted in suicide. Before allowing discussion, I then gave students their articles and explained how I wanted them to annotate, leaving the directions on the board. I set a timer for 5 minutes. That was not enough time, so I added another 5. A few students (my stronger readers) were finished within the first 5 minutes, but I wanted to give enough time for everyone to annotate fully.
I will allot 10-15 minutes for the articles in the future in order to encourage students to stay focused and help with timed reading training for final exams. (4th block had the most difficulty staying quiet after completing their initial reading.)
Students had to remain silent after completing their annotations which was easy for most of them in 3rd block. 4th block however had some issues. Although, some will have to remember not to write or play with materials while listening to others speak. The most trouble I had came from the sophomores in room 123 because they don't know how to not act like idiots when no one is watching them.
In the future, I will add to the instructions for the members to direct the rest of the group to the passage before reading in order to help those who need to read the section for better comprehension. I will also direct group members to be thinking about what their response will be when it is time for their discussion during the rest of the minute from the original speaker.
3rd block: I had students get out their phones and set a timer for 1 minute. That person was then in charge of resetting the timer for each speaker.
4th block: I tried to have students keep a timer. They could not handle this, so I had to be the one to maintain the timer for other member responses.
For the original member to respond, I will set a class timer in order to keep better timing on the group as a whole. I kept the timer hidden so students would not stare down the clock. I noticed many students stopped speaking way before the timer ran out. I was surprised that my big talkers and those who dominate the conversations definitely did not utilize a lot of their time.
3rd block: When having to sit in silence for the rest of the minute during response time, students were really good about monitoring the other students for speaking when they weren't supposed to. Overall, students discussed the material in a mature manner without much intervention from me on maintaining a respectful mien.
4th block: Had issues following directions in allowing only 1 person to speak at a time and waiting in silence. I had to stop and explain twice what I meant by not talking unless you were the person assigned to speak.
Silence is hard.
4th block: I had to have students clear their desks because they wanted to play with papers, read books, move notebooks around, just do anything else besides sit still and think. After repeatedly explaining that they just had to sit and listen, I still had some students trying to mime to one another, play with scarves, and write notes. There were a few girls that had some serious attitude issues and could not handle the silence.
Generally, 4th block finished with at least 1/2 the time left for each discussion piece, whether it was 1 minute or 2 minutes. 3rd block generally used more time for their discussions.
I love that each student was able to get a chance to respond without anyone else interfering their moment. This also gave students time to consider their responses without pressure from more vocal and outspoken students.
There were a few students I noticed that did not pay particular attention when other people were speaking. Coincidentally, these are also my lowest students.
My 3rd block had some issues reestablishing their focus with lunch interrupting their discussions. It took some time getting back on track. Students were writing notes on paper to each other, among other things, and I had to redirect their attentions.
Consistently, students used only 1 of the 2 minute response times that they were allowed in order to respond to others' points and explain why they chose their particular passages.
Because I ran out of time 3rd period and could not do the Gallery Walk, I decided to take the comments down and assign numbers for each question. I am going to give each group a question and the corresponding post it notes and have the students organize and share their findings in class.
____________________________________________________________________________
After the silent group work, I asked for students' feedback. Some feelings were (and these come from my outspoken students, the ones who always raise their hands and want to speak):
Cons:
"It's too hard to remain focused when it's so quiet."
"It's easier to think when everyone is talking."
"I didn't have enough time to give my opinion."
"It's hard to wait and remember my ideas when someone else is speaking."
"I couldn't congratulate someone when they had a good idea."
"Couldn't respond immediately to another person's thoughts."
"Silent time felt awkward."
"Didn't get to have a class discussion. Made it boring not involving the whole class."
"If you did agree and have the same answer, not much to add."
"Repeated same answers in small group so ran out of things to say."
"Got fidgety during silence."
"Misunderstandings and couldn't fix it until it was your turn to speak again."
Pros:
"It gives everyone a chance to speak without being interrupted."
"Learned how to listen to others."
"Able to hear how other people felt on the subject."
"Learned what other people are thinking and compared to your thoughts. See different opinions/mind sets."
"Kept on task w/specified times."
"Able to share your thoughts w/out fear of judgment."
____________________________________________________________________________
Side note: My 4th block came in and said my 3rd block felt as if the discussion activity was so boring they wanted to sleep. Coincidentally, students are afraid of silence and having to speak their opinions. Additionally, I want to use a chart to diagram length of responses from students to record general response times and compare them to whole group discussions.
I will also assign a "talk monitor" to help dissuade others from speaking during silent moments.
I definitely got frustrated with the students during this activity.
Post-It notes do not stick to the walls.
Thursday, October 2, 2014
Discovering The Unit Circle
In Pre-Calculus, a HUGE HUGE HUGE chunk of the curriculum is trigonometry. With this, students must know and understand the unit circle and how it applies to the trigonometry we are learning. When I was in high school, the unit circle was put on the board and we were told to copy it down and memorize it. Over the years, I've tried different activities.. paper plate unit circle, colored pieces of paper, and so on. It seemed to me that still telling them the circle and what to write down was not allowing the students to truly understand the unit circle and all of the patters associated with it. So, I decided to try something new with my lovely group of juniors.
I first split the students up into groups based on where they are sitting. I placed 3 students in a group and had them circle up so they could see one another. I then gave each group a blank unit circle in a sheet protector along with a dry erase marker. Then, I explained the modified version of "Save the last word for ME" that we used.
"I will be the timekeeper and 1 student in each group will be the facilitator. Students will number off 1, 2, 3, etc. Person number 1 will have a set amount of time to start labeling what they know of the Unit Circle. They will have to explain why they labeled what they did, however the other 2 members may not speak. After the time is up, the other two members have a set amount of time to discuss, agree, or fix what the first member added. Then, we will go to member 2 and follow the same protocol. This will be done through the following key ideas.
*Label Degrees (1 minute; 1 minute)
*Label Degrees (1 minute; 1 minute)
*Label Radians (1 minute; 1 minute)
*Label 1st Quadrant Coordinates (2 minutes; 2 minutes)
*Label 2nd Quadrant Coordinates (2 minutes; 2 minutes)
*Label 3rd Quadrant Coordinates (2 minutes; 2 minutes)
*Label 4th Quadrant Coordinates (2 minutes; 2 minutes)
*Label 1st Quadrant Coordinates (2 minutes; 2 minutes)
*Label 2nd Quadrant Coordinates (2 minutes; 2 minutes)
*Label 3rd Quadrant Coordinates (2 minutes; 2 minutes)
*Label 4th Quadrant Coordinates (2 minutes; 2 minutes)
*** COORDINATES MUST BE EXACT! NOT ROUNDED! ***
** Students should look for trig function relationships during this time **"
** Students should look for trig function relationships during this time **"
These rules were displayed and each task was displayed on the SmartBoard one at a time.
At first, students freaked out when they saw they had to complete the entire unit circle. They felt better when I told them they would fill it out piece by piece. Students were great in the silence and focused on watching what the writer in their group was doing. I could tell it was hard for some students to just sit without being able to correct their group mates right away. Some students got ancy and were dancing in their seats when they had to remain quiet. The labeling of the degrees and radians went well overall. Students noticed the patterns easily, especially since we had discussed the quadrant angles before. The coordinates were a little more difficult. Some groups had absolutely no idea, and they didn't know how to find the exact coordinates (the coordinates are irrational... they can't easily be converted into pretty fractions). I had to guide the groups along a little bit (by giving them hints about drawing right triangles and do a mini-lesson on simplifying radicals), but again they quickly saw the patterns and were able to continue with the process.
I really liked this process for students discovering/learning the unit circle. It really required them to think about how the things we had learned applied to the unit circle. They were tired and had headaches after, but that means they really worked hard in class that day. A few of them even said they liked that better than just seeing and copying the unit circle.
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