So since they are cutting my calculus class down to 5 periods a week to make room for a humanities class that means I would only teach 15 periods (periods are 45 mins.). My company requires that I teach at least 20 periods. So next year I will be teaching a math competition class. I will have the students solve problems from previous AMC tests to prepare for the AMC test in February. I will most likely meet each class for one period a week. So that will mean I am teaching 18 periods a week teaching math and then add the two periods a week that I am glee club adviser and I will be at 20 periods a week. I am hoping that it will be an optional course for my top students. The lower students will really struggle with the content and I will have trouble ensuring that they succeed.
I plan on having the students prepare for the AMC first semester and then prepare for the Euclid contest in March. I know students can get involved with writing the exams. I am not sure how that is done and will have to look into it. If so I will add that as part of my class and make an assignment to be write a question for the exam. I may still include the assignment of writing your own question even if I can't arrange to have the students take part in the writing of the exam.
Grade break down:
Final: 20%
Quizzes/Midterm: 30%
Presentations: 30%
Homework: 10%
In-class: 10%
For the final exam and midterm exam I will have to find some full exam of the test. I don't want to cobble together questions and want to save the sample questions for in-class use. I will have to look for an exam to use and write it after the AP test.
I was going to have one quiz a week so the students get practice on the questions. I will be using the Mathematical Association of America's archive of questions to make the quizzes. I was planning on using the sample brochure questions to make the quiz. They have about five questions that gives a good overview of the test. Here is one example. I will have to look at the scores at first, but I will have to find a curve to use. I assume that the students will struggle with these questions. I could give them the same amount of time on the quiz as they will on the test which is three minutes per question and then curve the quiz like crazy since they most likely not finish. That means about 15 minutes for the quiz which I can fit in each week. However I could give them 45 minutes to finish and might not have to curve it as much. So I could do it so I have a quiz every other week.
I was going to make this class presentation heavy since the class is just about solving questions to prepare for the exam. I thought about lecturing some myself, but since the topics that are presented are so wide and cover a lot of different things I wouldn't know where to start. I will use wolfram alpha articles to supplement students understanding. However I need something that can define advanced math topics in simple language since my students are in high school and second language learners. I might look into getting a copy of the textbook my professors use for Contemporary mathematics since that course covers a lot of random advanced math topics. So I think one week I will assign problems to pairs and let them work on it. They can discuss with me as they solve it. I will have students sign up for days they want to present at the end of calss. I will monitor how much work they get done and maybe give them another day in class to work on the problem. Then the next week I will have a quiz. Then the following week have presentations start. Then rotate between presentations and quizzes until we finish the presentations.
So 1-2 weeks spent preparing, then rotate the weeks between quiz and presentation for 7 weeks (based on having 28 students in a class). If I have a smaller class I will rotate between quizzes and presentations until presentations are done, then restart the cycle.
I was going to use the worksheet set of problems for presentations, for example this one. The questions are labeled with their difficulty at the bottom. If the class is required for all of my students then I will give the weaker students the easier problems and my stronger students the more difficult problems. If it is an optional course I may keep a record of who has presented what level of question. I will make sure students get chances at each type. If I can't find a full exam somewhere to use for my final and midterm then I will have to use these questions, but I really want to save these for presentations.
During presentations I will grade the group/individuals using the following rubrics.
General Rubric
Detailed Rubric
If I have a class of 28 I will do groups of two and I will grade each person individually doing my best going between the two different rubrics. If we make it optional and the class is really small I might have individual students present one problem. However those in the class will grade one of the individuals in the group using the rubric. I might also have some people in the audience circle one of the ten areas to improve from this article. Then I think I will make some sort of exit slip they have to fill out. I will check that they are giving good feedback and filling out all of these forms. They will get a score for the feedback that they provide and will be a part of their in-class grade.
I was not going to assign homework for this class, because I did not know what I would use for homework since I was using the worksheets for presentations. However someone from the Center for Education in Mathematics and Computing (CEMC) at the University of Waterloo spoke to my students. He mentioned a problem of the week that you can subscribe to. So I think I will assign the students the problem of the week as homework. I will require them to show any work that they can on the problems and that they don't have to get the right answer, but just try the problem. So to grade them I will quickly scan them to see that they have tried. I think it will be easy to see who tried and who didn't. For those who tried they will get a 5 and those who didn't will get a 4.
I am not sure whether I will give them the 9/10 or 11/12 question. I want to keep my grading load low so I don't want to assign two questions. I may just decide which question is more interesting or more linked with the AMC. This will be a course for 11th graders, but I worry about giving them that question because of their English level.
For the Euclid Contest/Second Semester:
I think for this there is enough questions in the archive to pull from for my midterm, final, quizzes, and presentations. Although there is a resource manual that I can buy to supplement the class and most likely use questions from it for quizzes if need be. I will have to talk to my school/company about getting that paid for by them. I could also buy it with my own money so the resource is mine to continue using. It is not too expensive.
I would still continue giving the students the problem of the week as homework in the second semester.
We are required to give the students homework over the Chinese new years vacation which is three weeks long. I may give them two problems to solve over that break both the problem of the week for the 9/10 grade and the problem of the week for the 11/12 grade.
Also the Euclid contest is in March. So I could include more Euclid stuff until the exam in March. I will have to give a full Euclid test before the actual one and will most likely have to schedule that in my own class time. I will have to talk to my principal after that. The Chinese system is still very test driven and my students may not enjoy the math unless there is a test waiting. We could work on writing and solving our own questions after the tests are over. The midterm and finals will land after the competition tests are over in the second semester. So for the midterm and final I could give them another test based off of questions from the archive even though they are done taking it. That will really effect the course.
So there is still a lot up in the air about this course. However I wanted to brain storm and get an idea for the general structure and get my resources for the course gathered together. A lot will have to be passed by my principal and the Chinese staff here at the school before anything is final. I am excited about it because I think it is going to be very interesting. I think for my stronger math students it might be the first time they are really and truly challenged. However they always seem to rise to the occasion and excel at any question I give them.
About Me
- DominiqueL
- I love to teach and I love math. Teaching has always been a passion since I was in 5th grade. I gained a love of math later in eighth grade. I have been told that I always have a smile on my face and a song in my heart which is the best description of me.
Saturday, April 6, 2013
Friday, March 8, 2013
Math Notebooks
I have thought of trying to incorporate writing and notebooks for a long time in math. I thought this was a way to make math more fun. I also thought this was a way to engage students in math using another type of intelligence. I hoped to engage the eloquent writers to express their understanding of math using the medium they are most comfortable with.
This was a major focus during my work towards my masters. I have been able to include more activities in my math class where students write down responses on their individual whiteboards. I still want to include more writing assignments though, but have trouble balancing computation problems with writing problems. I still want to find a way to work more writing assignments into my curriculum, but I have focused on keeping good class notes in the students notebooks.
Although after writing this blog post a thought occurred to me about how to incorporate more writing (ah the power of writing/blogging). When I start a new chapter with the students I use a directed reading thinking activity (DRTA). I ask the students what they think the title means. I ask them what they think they will learn based on the title. Then I have them look at the picture at the beginning of the chapter and the example problem that relates to it. I ask them how the two are related. I ask them to think about how you would solve the example problem. Some students get really carried away and want to know how to solve the problem that second. I then ask them how the example problem relates to the title and what we will learn in this chapter. I then have them read the title of the first section of the chapter and ask them how it relates to the title of the chapter. Then I ask them what they think they will learn in the chapter. I have them read and write their answers on their personal whiteboards. Sometimes I do a think, pair, share to answer these questions. However I ask students to show their whiteboards to the class and call on students to share with the class. I keep a list of ideas after each round on the chalkboard at the front of the classroom. As a class we compare answers and as we get more information we can see if our predictions were right. Often to wrap up this activity I read the summary of the chapter to the class which confirms and denies the predictions made. I often will read it and say this is just what student X said. This activity helps them learn to make predictions by looking at titles, pictures, and other text. I encourage students to use the strategy in other classes. It also helps build background for the students and helps me understand how much they have studied. It also helps make connections from past material to the new material. I think to build even more background I think I will do a writing activity after the DRTA. I will have the students answer a question on their whiteboard. The question will be the big idea of the chapter. I think I will then have students respond to the question again on the weekly quiz. This way they have several drafts to use before the final and they will have another chance at answering once they have learned some of the content. I will provide feedback on the written part. They should have two quizzes before the end of the chapter so they will have two chances to practice their answer. Also if for some reason a lesson runs short and I have extra time then I can have students write and/or discuss that chapters prompt. Then once we have finished the chapter they will write their final response on the page right after that chapters notes in their notebooks. I will have to instruct them carefully to save a page or two for that chapters journal entry. Although as long as they include it somewhere in their notebook and list the journal entry in their table of contents then I guess it won't matter. It just would be nice to have all the notes on that chapter followed by the journal entry over that material.
I hope that this helps the students express themselves better on the free response questions of the AP test. They are putting more and more emphasis on explaining the answers with words. The questions are really looking for calculus with words. This has proven difficult for my students since English is their second language. I also hope if they can explain a process or concept in general using the words they can solve any problem.
I will need the AP scores to back this up. The company and the Chinese administration put a lot of pressure on getting high scores. This is doubly true in math since all of the students excel in math, so they except a 5 out of 5 for all the students.
Here are the prompts I am thinking of using. I got most of these from the assessment resource book that accompanies the calculus book by Finney, Demana, Waits, and Kennedy (3rd edition) (citing my source). Some are the writing to learn question in the books exercises. Some I have tweaked or added to.
Chapter 1 (Pre-Calculus and Review of all Types of Functions): Explain why a function that is not one-to-one does not have an inverse function.
Chapter 2 (Limits and Continuity): Explain the importance of continuity in discussing limits. Also discuss the value of determining limits as x approaches infinity. For example in economic problems, the limit of a function can give important information. If a company has an increasing revenue or profit function, what does the limit as x approaches infinity tell us?
Chapter 3 (Derivatives and Differentiability): What does the derivative represent? Use the concept of the derivative to define what it might mean for two parabolas to be parallel. Construct equations for two such parallel parabolas and graph them. Are the parabolas "everywhere equidistant", and if so, in what sense?
Chapter 4 (More complicated Derivatives): How does the chain rule help us find the derivatives of almost any function? Why is implicit differentiation useful in examining the derivatives of curves that are not functions?
Chapter 5 (Applications of Derivatives): Think about the importance of the second derivative test. In economic applications, what does the second derivative test reveal about cost functions and revenue functions? And why is that information important?
Chapter 6 (Integration): Let f be a positive continuous function that is concave up. If the trapezoidal rule is used to estimate an area between f and the x-axis, will the result be an overestimate or an underestimate? What if the midpoint rule is used instead? Explain how you know if it is an overestimate or underestimate. (often a question on the AP test)
Chapter 7 (Integration Techniques and Differential Equations): Compare and contrast non-separable differential equations with separable differential equations. Analyze the following: equations, solution method/process, how to use initial conditions, and slope fields. Use the following vocab words: general solution, particular solution, initial condition, non-separable differential equation, separable differential equation.
Chapter 8 (Applications of Integration): Describe in what situations should you use the disk method, washer method, and shell method? Think about rotating the same curve about the y-axis and the x-axis. What similarities could be seen about the volumes of these solids? Are they the same? Would you use the same method to find the volume?
Review: The students will write about the mathematicians we have studied going to a dinner party and talking about the topics we have studied so far. The assignment will let them be creative and help them review concepts. I will give them guidance on what to write about, but still the ability to choose and be creative. I am really looking forward to reading these.
I came up with the review entry after taking a ESOL class online from Willamette. The example came up in the textbook we were using for the class and was tailored to an English class. The example was student writing about author's from a certain time period at a dinner party. I read that and thought why can't it be about mathematicians. The textbook I use for calculus has some really interesting comments about the different mathematicians for example it talks about how Michel Rolle spent a long time making fun of Calculus, but then ended up having contributing a theorem (Calculus, Finney, Demana, Waits, and Kennedy, 3rd edition). So I flipped through the book to see who else was mentioned and for other paragraphs that mentioned the mathematicians contributions. I had fun actually reading my Calculus textbook and finding little gems in it that I had previously skimmed over.
The one for Chapter 7 I came up with by myself. I noticed last year that my students could not put the equations with the vocab. They could solve a separable differential equation no problem if you put it in front of them, but if you asked them to describe what they did using the above vocab then they couldn't. The differential equations questions on the AP test are loaded with the vocab I listed. I put more emphasis on the vocab this year and had students write "a comparison essay" as homework comparing non-separable differential equations and separable differential equations. I got some really creative pieces. I think it helped solidify the vocab so when they saw it on the test they knew what the question was talking about. Most of the students could describe how to solve a separable differential equation at the end of this year, but there was still a few that did not know. They were the few that struggle normally though and was not shocking to see that they did not know, but it was disappointing Although hopefully now after reviewing what the words mean before the AP test they will do well on the free response question that is over separable differential equations. It just shows that some students need constant reminder and review for the words to sink in.
I suggest that if you want to do something similar look through the assessment resources that come with your textbook. Hopefully I can continue this if I go on to teach other subjects and out of other textbooks. I would need some ideas for writing prompts at least as a start. So hopefully other books come with alternate assessment ideas in the resource books that accompany it.
I think the dinner party review assignment can be done in any math class at any level. Most math textbooks include short biographies on mathematicians. You could also turn it into a sort of mini research project. You just have to suggest topics or people that relate or connect to your content. So I think the hard part would be to come up with suggestions for students to write about because that would take some time on your part to research the background of the math you are teaching.
I plan on reading these and checking these journal entries when I collect the notebooks. I will just have to figure out how to grade them. I think I can use part of the rubric I use for mathematical presentations and then I studied rubrics to use with ESL students in some of the ESOL classes I took online. I will have to look back through the textbook I have to find a rubric that will work. I want it to be something quick and easy to use. Any suggestions or links to rubrics would also be greatly appreciated.
Let me talk about what I have done with the notebooks so far and what I plan to do.
During my student teaching I had students keep a table of contents for their notebooks and number the pages in their notebooks. I thought this kept things organized and if their was something specific they needed to study they could easily find their notes on that subject. It also makes grading them easy because then you know which page to turn to when you are grading something specific. I continued that work with my Chinese students. Some students are good about doing this and others have not. I just have the students label what part of the textbook we are working on and use the title of the section from the textbook. I always have this displayed on the first slide of that day's powerpoint. Some students leave an empty line between each entry and others leave extra space when they start a new chapter. I also have a student that put in tiny stick notes on the pages where each new chapter starts in her notes.
I started working with my students on using an organized system for their notes during my student teaching and I tried a couple of things. This year I focused on using a Cornell notes like set up. The students put the main idea of the content or summarize what the notes on the right are about. So they could put the name of the theorem in a small column on the left of notes and in the large section on the right they could have the theorem written out. I gave students this main ideas at the beginning and then wanted students to come up with them on their own. I wanted them to either come up with them in class so they are processing information during class. The other option being they review their notes and add the main ideas in the left. I noticed once I was not giving them specific main ideas students were either not including them or giving really general main ideas. Some students would just write example, but not what it was about or why it was different. Some would just write equations and I really wanted them to use words to summarize the notes. Last year I found when I handed out study guide sheets that listed the objectives to be tested on the exam the students did not know the English words connected to the math that they knew. I could put a problem in front of them and they could solve, but if I asked them to describe what type of problem it was using words they couldn't. I hoped to solve this problem by having students include some of those words in the main idea column.
I don't want to feed them the main ideas in class either on the whiteboard or on the poweroint because I think they gain a lot more learning coming up with them on their own. I have one student who always asks how to classify what we are learning so she can label it in her main idea column, but only a few students listen to my answer. I am not sure how to help them develop more specific ideas. I wonder if I could stop and ask them what we are learning on this slide and how it relates to what we have been doing? It could be a way to check in with students and the class about their understanding and help them come up with main ideas.
Then they use the bottom five lines of the page to make notes about tips and strategies for the AP test. I often remind them or give suggestions of things to do on the AP test. I began writing these tips on the board and then expected them to listen for them. I noticed a lot of people stopped writing them down. I need to get the kids to recognize that when I say AP test that should be a cue to them to use that bottom part of the page.
I have a part on my rubric that talks about underlining, highlighting/color coding, starring, boxing, or using other techniques to make information stand out. However still were not make the big key concepts like formulas,derivative rules, vocab, or even titles stand out. So I think I need to mention that and go over that more. Although when I first started in Chapter 1 and 2 I talked about it a lot and modeled it some. However maybe I need to give more reminders. The students can do this during class or after class when they are reviewing their notes. Some of my students have really found a way to make color really effective and organize their notes.
I also wanted students to relate or connect ideas in their notes. For example how derivative equations of different trig functions relate. They could also relate to things they learned in physics. They can connect definitions to examples. I don't think I gave them enough examples of this. I think next year I will bring some of the best notebooks from this year to illustrate to the next years class what I am talking about. I think I will have to make photo copies so I will always have examples to go along with my rubric.
I just recently finished grading the notebooks and was sick of finding handouts shoved willy nilly in them. One student had English handouts in their notebook. I made a comment about that, but no one listened. I think next year I will take away one point from the format category for having loose papers or handout in their notebook. I have had some students who taped or glued my study guide handouts in their notebooks after that chapters notes, but they listed it in their table of contents and it was placed in a logical place.
Rubric
I took most of the rubric from the AVID programs rubric, but I added some of my own ideas that tailored to math and what I wanted. I also got rid of categories that I thought didn't really lend itself to math. I told the students the AVID program uses a similar rubric and those are some of the best students who are working hard to go to college. I told them they start doing this in 7th grade and they were shocked. It showed them that other people in America felt you needed these tools in college. They seem shocked and impressed at first at least.
Now let me explain how I use the rubric. I circle each numeral in each category. So this means that students could get a 5 for using plenty of space between their notes, but a 3 because they are not using abbreviations. This way the students can see how well they are doing on each skill. Then what I do is I average the score in each category. I always round up to the nearest tenth. Then I added up the averaged score in each category and then find an average for the overall score. So it is only worth 5 points in the end. This way they get a wholistic score on the notes. I have debated about averaging in each category then making the notes 20 points (5 points for each category), but I am not sure if that is too much. Next year I hope to grade the notebooks every three weeks until I have looked at notes for each chapter. So that means that in total that will be 40 points for the notebook. Although next year I am putting more weight on the scores so I should probably keep the points low. I have also thought about finding the average score between all four categories then multiplying by ten so there are no decimals. Then each chapter would be worth 50 points, but that seems too much. I will have to think it over.
The scores are often low using the rubrics since I am holding them to high expectations. I often will curve the grades or give back points in the end. I often find to when I start grading them I start mean and become more lenient. So if I go back and give more points it evens things out. However some students rise to the high expectations and take amazing notes. I recently let those students have extra credit because they took such good notes. I am not giving too many extra credit opportunities this year so I thought this would be a good chance to get some extra credit.
After I graded their notebooks the first time I gave them some written feedback to improve which described some examples. I will have to give this type of feedback more often next year. I will probably give this to the students every three weeks or every month. We finish a chapter a month usually so that will help them refine their notes for the next chapter.
This was a major focus during my work towards my masters. I have been able to include more activities in my math class where students write down responses on their individual whiteboards. I still want to include more writing assignments though, but have trouble balancing computation problems with writing problems. I still want to find a way to work more writing assignments into my curriculum, but I have focused on keeping good class notes in the students notebooks.
Although after writing this blog post a thought occurred to me about how to incorporate more writing (ah the power of writing/blogging). When I start a new chapter with the students I use a directed reading thinking activity (DRTA). I ask the students what they think the title means. I ask them what they think they will learn based on the title. Then I have them look at the picture at the beginning of the chapter and the example problem that relates to it. I ask them how the two are related. I ask them to think about how you would solve the example problem. Some students get really carried away and want to know how to solve the problem that second. I then ask them how the example problem relates to the title and what we will learn in this chapter. I then have them read the title of the first section of the chapter and ask them how it relates to the title of the chapter. Then I ask them what they think they will learn in the chapter. I have them read and write their answers on their personal whiteboards. Sometimes I do a think, pair, share to answer these questions. However I ask students to show their whiteboards to the class and call on students to share with the class. I keep a list of ideas after each round on the chalkboard at the front of the classroom. As a class we compare answers and as we get more information we can see if our predictions were right. Often to wrap up this activity I read the summary of the chapter to the class which confirms and denies the predictions made. I often will read it and say this is just what student X said. This activity helps them learn to make predictions by looking at titles, pictures, and other text. I encourage students to use the strategy in other classes. It also helps build background for the students and helps me understand how much they have studied. It also helps make connections from past material to the new material. I think to build even more background I think I will do a writing activity after the DRTA. I will have the students answer a question on their whiteboard. The question will be the big idea of the chapter. I think I will then have students respond to the question again on the weekly quiz. This way they have several drafts to use before the final and they will have another chance at answering once they have learned some of the content. I will provide feedback on the written part. They should have two quizzes before the end of the chapter so they will have two chances to practice their answer. Also if for some reason a lesson runs short and I have extra time then I can have students write and/or discuss that chapters prompt. Then once we have finished the chapter they will write their final response on the page right after that chapters notes in their notebooks. I will have to instruct them carefully to save a page or two for that chapters journal entry. Although as long as they include it somewhere in their notebook and list the journal entry in their table of contents then I guess it won't matter. It just would be nice to have all the notes on that chapter followed by the journal entry over that material.
I hope that this helps the students express themselves better on the free response questions of the AP test. They are putting more and more emphasis on explaining the answers with words. The questions are really looking for calculus with words. This has proven difficult for my students since English is their second language. I also hope if they can explain a process or concept in general using the words they can solve any problem.
I will need the AP scores to back this up. The company and the Chinese administration put a lot of pressure on getting high scores. This is doubly true in math since all of the students excel in math, so they except a 5 out of 5 for all the students.
Here are the prompts I am thinking of using. I got most of these from the assessment resource book that accompanies the calculus book by Finney, Demana, Waits, and Kennedy (3rd edition) (citing my source). Some are the writing to learn question in the books exercises. Some I have tweaked or added to.
Chapter 1 (Pre-Calculus and Review of all Types of Functions): Explain why a function that is not one-to-one does not have an inverse function.
Chapter 2 (Limits and Continuity): Explain the importance of continuity in discussing limits. Also discuss the value of determining limits as x approaches infinity. For example in economic problems, the limit of a function can give important information. If a company has an increasing revenue or profit function, what does the limit as x approaches infinity tell us?
Chapter 3 (Derivatives and Differentiability): What does the derivative represent? Use the concept of the derivative to define what it might mean for two parabolas to be parallel. Construct equations for two such parallel parabolas and graph them. Are the parabolas "everywhere equidistant", and if so, in what sense?
Chapter 4 (More complicated Derivatives): How does the chain rule help us find the derivatives of almost any function? Why is implicit differentiation useful in examining the derivatives of curves that are not functions?
Chapter 5 (Applications of Derivatives): Think about the importance of the second derivative test. In economic applications, what does the second derivative test reveal about cost functions and revenue functions? And why is that information important?
Chapter 6 (Integration): Let f be a positive continuous function that is concave up. If the trapezoidal rule is used to estimate an area between f and the x-axis, will the result be an overestimate or an underestimate? What if the midpoint rule is used instead? Explain how you know if it is an overestimate or underestimate. (often a question on the AP test)
Chapter 7 (Integration Techniques and Differential Equations): Compare and contrast non-separable differential equations with separable differential equations. Analyze the following: equations, solution method/process, how to use initial conditions, and slope fields. Use the following vocab words: general solution, particular solution, initial condition, non-separable differential equation, separable differential equation.
Chapter 8 (Applications of Integration): Describe in what situations should you use the disk method, washer method, and shell method? Think about rotating the same curve about the y-axis and the x-axis. What similarities could be seen about the volumes of these solids? Are they the same? Would you use the same method to find the volume?
Review: The students will write about the mathematicians we have studied going to a dinner party and talking about the topics we have studied so far. The assignment will let them be creative and help them review concepts. I will give them guidance on what to write about, but still the ability to choose and be creative. I am really looking forward to reading these.
I came up with the review entry after taking a ESOL class online from Willamette. The example came up in the textbook we were using for the class and was tailored to an English class. The example was student writing about author's from a certain time period at a dinner party. I read that and thought why can't it be about mathematicians. The textbook I use for calculus has some really interesting comments about the different mathematicians for example it talks about how Michel Rolle spent a long time making fun of Calculus, but then ended up having contributing a theorem (Calculus, Finney, Demana, Waits, and Kennedy, 3rd edition). So I flipped through the book to see who else was mentioned and for other paragraphs that mentioned the mathematicians contributions. I had fun actually reading my Calculus textbook and finding little gems in it that I had previously skimmed over.
The one for Chapter 7 I came up with by myself. I noticed last year that my students could not put the equations with the vocab. They could solve a separable differential equation no problem if you put it in front of them, but if you asked them to describe what they did using the above vocab then they couldn't. The differential equations questions on the AP test are loaded with the vocab I listed. I put more emphasis on the vocab this year and had students write "a comparison essay" as homework comparing non-separable differential equations and separable differential equations. I got some really creative pieces. I think it helped solidify the vocab so when they saw it on the test they knew what the question was talking about. Most of the students could describe how to solve a separable differential equation at the end of this year, but there was still a few that did not know. They were the few that struggle normally though and was not shocking to see that they did not know, but it was disappointing Although hopefully now after reviewing what the words mean before the AP test they will do well on the free response question that is over separable differential equations. It just shows that some students need constant reminder and review for the words to sink in.
I suggest that if you want to do something similar look through the assessment resources that come with your textbook. Hopefully I can continue this if I go on to teach other subjects and out of other textbooks. I would need some ideas for writing prompts at least as a start. So hopefully other books come with alternate assessment ideas in the resource books that accompany it.
I think the dinner party review assignment can be done in any math class at any level. Most math textbooks include short biographies on mathematicians. You could also turn it into a sort of mini research project. You just have to suggest topics or people that relate or connect to your content. So I think the hard part would be to come up with suggestions for students to write about because that would take some time on your part to research the background of the math you are teaching.
I plan on reading these and checking these journal entries when I collect the notebooks. I will just have to figure out how to grade them. I think I can use part of the rubric I use for mathematical presentations and then I studied rubrics to use with ESL students in some of the ESOL classes I took online. I will have to look back through the textbook I have to find a rubric that will work. I want it to be something quick and easy to use. Any suggestions or links to rubrics would also be greatly appreciated.
Let me talk about what I have done with the notebooks so far and what I plan to do.
During my student teaching I had students keep a table of contents for their notebooks and number the pages in their notebooks. I thought this kept things organized and if their was something specific they needed to study they could easily find their notes on that subject. It also makes grading them easy because then you know which page to turn to when you are grading something specific. I continued that work with my Chinese students. Some students are good about doing this and others have not. I just have the students label what part of the textbook we are working on and use the title of the section from the textbook. I always have this displayed on the first slide of that day's powerpoint. Some students leave an empty line between each entry and others leave extra space when they start a new chapter. I also have a student that put in tiny stick notes on the pages where each new chapter starts in her notes.
I started working with my students on using an organized system for their notes during my student teaching and I tried a couple of things. This year I focused on using a Cornell notes like set up. The students put the main idea of the content or summarize what the notes on the right are about. So they could put the name of the theorem in a small column on the left of notes and in the large section on the right they could have the theorem written out. I gave students this main ideas at the beginning and then wanted students to come up with them on their own. I wanted them to either come up with them in class so they are processing information during class. The other option being they review their notes and add the main ideas in the left. I noticed once I was not giving them specific main ideas students were either not including them or giving really general main ideas. Some students would just write example, but not what it was about or why it was different. Some would just write equations and I really wanted them to use words to summarize the notes. Last year I found when I handed out study guide sheets that listed the objectives to be tested on the exam the students did not know the English words connected to the math that they knew. I could put a problem in front of them and they could solve, but if I asked them to describe what type of problem it was using words they couldn't. I hoped to solve this problem by having students include some of those words in the main idea column.
I don't want to feed them the main ideas in class either on the whiteboard or on the poweroint because I think they gain a lot more learning coming up with them on their own. I have one student who always asks how to classify what we are learning so she can label it in her main idea column, but only a few students listen to my answer. I am not sure how to help them develop more specific ideas. I wonder if I could stop and ask them what we are learning on this slide and how it relates to what we have been doing? It could be a way to check in with students and the class about their understanding and help them come up with main ideas.
Then they use the bottom five lines of the page to make notes about tips and strategies for the AP test. I often remind them or give suggestions of things to do on the AP test. I began writing these tips on the board and then expected them to listen for them. I noticed a lot of people stopped writing them down. I need to get the kids to recognize that when I say AP test that should be a cue to them to use that bottom part of the page.
I have a part on my rubric that talks about underlining, highlighting/color coding, starring, boxing, or using other techniques to make information stand out. However still were not make the big key concepts like formulas,derivative rules, vocab, or even titles stand out. So I think I need to mention that and go over that more. Although when I first started in Chapter 1 and 2 I talked about it a lot and modeled it some. However maybe I need to give more reminders. The students can do this during class or after class when they are reviewing their notes. Some of my students have really found a way to make color really effective and organize their notes.
I also wanted students to relate or connect ideas in their notes. For example how derivative equations of different trig functions relate. They could also relate to things they learned in physics. They can connect definitions to examples. I don't think I gave them enough examples of this. I think next year I will bring some of the best notebooks from this year to illustrate to the next years class what I am talking about. I think I will have to make photo copies so I will always have examples to go along with my rubric.
I just recently finished grading the notebooks and was sick of finding handouts shoved willy nilly in them. One student had English handouts in their notebook. I made a comment about that, but no one listened. I think next year I will take away one point from the format category for having loose papers or handout in their notebook. I have had some students who taped or glued my study guide handouts in their notebooks after that chapters notes, but they listed it in their table of contents and it was placed in a logical place.
Rubric
I took most of the rubric from the AVID programs rubric, but I added some of my own ideas that tailored to math and what I wanted. I also got rid of categories that I thought didn't really lend itself to math. I told the students the AVID program uses a similar rubric and those are some of the best students who are working hard to go to college. I told them they start doing this in 7th grade and they were shocked. It showed them that other people in America felt you needed these tools in college. They seem shocked and impressed at first at least.
Now let me explain how I use the rubric. I circle each numeral in each category. So this means that students could get a 5 for using plenty of space between their notes, but a 3 because they are not using abbreviations. This way the students can see how well they are doing on each skill. Then what I do is I average the score in each category. I always round up to the nearest tenth. Then I added up the averaged score in each category and then find an average for the overall score. So it is only worth 5 points in the end. This way they get a wholistic score on the notes. I have debated about averaging in each category then making the notes 20 points (5 points for each category), but I am not sure if that is too much. Next year I hope to grade the notebooks every three weeks until I have looked at notes for each chapter. So that means that in total that will be 40 points for the notebook. Although next year I am putting more weight on the scores so I should probably keep the points low. I have also thought about finding the average score between all four categories then multiplying by ten so there are no decimals. Then each chapter would be worth 50 points, but that seems too much. I will have to think it over.
The scores are often low using the rubrics since I am holding them to high expectations. I often will curve the grades or give back points in the end. I often find to when I start grading them I start mean and become more lenient. So if I go back and give more points it evens things out. However some students rise to the high expectations and take amazing notes. I recently let those students have extra credit because they took such good notes. I am not giving too many extra credit opportunities this year so I thought this would be a good chance to get some extra credit.
After I graded their notebooks the first time I gave them some written feedback to improve which described some examples. I will have to give this type of feedback more often next year. I will probably give this to the students every three weeks or every month. We finish a chapter a month usually so that will help them refine their notes for the next chapter.
Tuesday, March 5, 2013
My Calculus Class Next Year
I have decided I am sick of grading homework and want to give more meaningful homework next year. So I am restructuring my class. I thought of this over vacation and wanted to get it down in front of me. I will work on creating and adjusting resources for next year after the AP test is over.
The equations I plan to use are listed in the assignment table chart that you will find with each project. I decided to have students focus on intervals when doing the second project so that they would have to check the endpoints when looking for extreme values. The classifications column is where I labeled the equation as easy(E) or hard(H). The other numbers and letters refer to groupings. The numbers all refer to equations of the same family. The letters that accompany them match together equations that are similar and often differ by a sign change. Each student in the class will get a different equation but this chart will help keep track of the students in the other classes that have the same function. When I assign functions I will type in their names.
The other project that will go into the project grade will be the review project I started doing last year. I started it to help students review for the test and to help students work on their English presentation skills. I think I will give them a copy of this article and discuss it before presentations begin so they can focus on how to improve their presentation skills. I will pass out a packet of old free response questions from college boards website. I give this to them a month or so in advance. I remind them to keep working on them. I also give them some time in class to work on them. Then around the end of march or beginning of April I have students pick which problem they want to present. This allows them to choose a problem they are comfortable explaining to the class. Then they have to give a ten to fifteen minute explanation of the problem to the class. This means they have to solve the problem using multiple methods, explain every step, explain how to solve on the calculator, or explain key things the college board is looking for when grading to fill the time limit. I grade them both on content as well as presentation skills. I want them to review the material, but I also want them to work on their presentation skills. I had to give presentations in several math classes and as a part of my major. They will have to present to future colleagues as well. I made a rubric to grade this by combining a lot of different rubrics I found online. Feel free to use in your classroom or adjust what I have made to use in your classroom. I will be trying out a new rubric next year. It is based on the one I used before however I added more emphasis on the math content area. So I increased the point value in the content area. I ran into a problem this year where students solved the problem using a second method, but that method was not really appropriate for the AP test. I didn't mind them including those solution methods, but they should have included information about which method to use on the test. I added that to compare methods as well. I also added a category about making sure the students explain why they can use a certain theorem. The students need to know that they can only use theorems when the function is continuous. The AP test often has questions where you can't use a certain theorem and must explain that you can't because the function is not continuous. So I hope by including this category it will prepare them for those type of questions.
General Rubric
Detailed Rubric
This year I am going to get the audience more involved. Three students will grade the students using this rubric. Then three other students will grade the solution of the problem using the AP rubric. I will also require students to ask one question during the course of the presentations. I wanted to make it more than one, but was not sure if I made it more that there would be time for all the students. I was going to check this off and put it in the grade book.
I will look at their feedback and check that they are doing it to give them a feedback grade that will go in the in-class category. I will check off who has asked a question and give them points for that in the in-class category.
I will average the scores given by the students using the AP rubric and put that score in the homework category.
I have also considered averaging the students scores on the presentations with mine.
I made a rubric to grade students notes and taught the students how to take good notes this year. I wanted to grade and collect the notebooks a lot, but did not have time since I was spending it grading everything else. I have also learned that I can only grade one class set of notebooks in one week. So I think each week I will collect the notebooks of one class. That way I am grading and giving feedback on their notes every three weeks. I will talk about how I grade notebooks and what I have discovered so far this year in another post.
For the in-class portion of the grade I will grade any activities that are done in class. However next year I am planning on using an app called class dojo to monitor student behavior and participation. One of my colleagues here in China uses it with his classes. He gives points for things like critical thinking and takes away points for speaking Chinese. At the end of the six weeks he looks at the summary points and gives them the grade according to that. I have to decide what criteria I will be looking for. I will also have to make sure I can use the app in the classroom since their is no wifi and the internet. I know it can be done, but I will have to test it out before I use it next year.
Here is my criteria:
Positive:
Different solution method
Critical thinking
Questions
Helps others
Negative:
Unprepared
Speaking in Chinese
Off task
I want to make these categories meaningful. I am try to think about what behavior in class makes a good math student. I would love more suggestions of categories to add.
I will try to keep you updated on how using class dojo impacts my classroom.
Grade break down:
Final: 20%
Tests/Midterm: 30%
Quizzes: 15%
Projects: 15%
Notebooks: 10%
In-class: 10%
This year I tried doing a project that helped students prepare for a free response question as well as develop their ability to explain their reasoning using different methods. The AP test emphasizes understanding the material using a graph, algebra, tables of values, and words. I started off with a project at the beginning of the year to help students work on justifying their answers using those methods. The project covered concepts that we had recently covered, but it also included concepts they need to review because we were going to explore them deeper. I enjoyed the sort of review and preview of material this year. So I will do the project again this year. However the students procrastinated on it. So I need to break it down some more. So each week they will have a small piece of the project to work on. So they will have to find the domain, range, x-intercepts, and y-intercepts of their given function. Then support their answer using a graph, table of values, algebra, or words. The problem I had this year was I couldn't grade the homework as well as the projects. Now the projects will be my main assignment to grade. I think this may be harder to grade than the homework out of the textbook I have been giving, but I think it will help them prepare for the AP test better. They will be preparing for the free response questions that are what most of my Chinese students do poorly on. They will also be developing analytic skills that will help them in other disciplines as well as their future math skills. Some of my students really wanted to attack the problem using each and every method. So they were developing the ability to view the problem in different ways and using different information. I will collect these each week and try to get them handed back in a week. Then at the end of the project I will take time in class to have students peer review the projects. Each student in one section of the class will have a different equation to analyze. The more advanced students will be given more complex equations and the weaker students given a less complex equation. So then I will take the projects of the students who studied the same equation in the different classes and have them grade each others paper. I hope the students will learn a lot from grading the other students paper and give good feedback. I think I will then take a quick glance at the projects and the scores. However I think I will just average the scores that were assigned by the students. I will include in the in-class category points for giving good feedback. So if a student did not provide enough comments, reasons, or the scored was not at all accurate then they will loose points. I will have to outline what good feedback is and have the students take it seriously.
I plan at the beginning of the year reviewing basic properties of functions: domain, range, intercepts. Then I will have them apply the knowledge they just learned: continuity and using limits to find asymptotes. Then I will have the preview/review material we will learn about in more depth later: increasing, decreasing, concave up, and concave down. The resources include handout describing the task, detailed rubrics outlining how to get the points, and a rubric grading sheet for each small piece of the project as well as the final project.
So the students will work on this project in September and October. It may even extend into November. I will see how small I can chunck up the project.
Project 2: Connecting a Function to its Derivatives
Sometime in November I should wrap up teaching about derivatives. Once that is over I am going to have the students start the next projcet. The students will have to find the derivative and second derivative of the function then apply them. They will have to find the local extreme values using both the first derivative test and the second derivative test. They will have to find the absolute extreme values. They will have to find the point of inflection and justify it. They will have to find where the function is concave up and concave down. I will require them to use the words to support their algebra. I will make sure they show all their algebraic work as well. These sort of questions are always in the free response section of the exam. I will give a lot of feedback about if they have justified their answer enough for the AP test on this project. I know that my students can determine where the function has these propeties, but they do not know how to support their answer using words or showing enough work. The resources include handout describing the task, detailed rubrics outlining how to get the points, and a rubric grading sheet for each small piece of the project as well as the final project.
Project 2: Connecting a Function to its Derivatives
Sometime in November I should wrap up teaching about derivatives. Once that is over I am going to have the students start the next projcet. The students will have to find the derivative and second derivative of the function then apply them. They will have to find the local extreme values using both the first derivative test and the second derivative test. They will have to find the absolute extreme values. They will have to find the point of inflection and justify it. They will have to find where the function is concave up and concave down. I will require them to use the words to support their algebra. I will make sure they show all their algebraic work as well. These sort of questions are always in the free response section of the exam. I will give a lot of feedback about if they have justified their answer enough for the AP test on this project. I know that my students can determine where the function has these propeties, but they do not know how to support their answer using words or showing enough work. The resources include handout describing the task, detailed rubrics outlining how to get the points, and a rubric grading sheet for each small piece of the project as well as the final project.
The following semester I will have the students work on a similar project but the equation that they will be given will be the equation from the previous semester, but with an integral. They will have to use the fundamental theorem of calculus as well as what they learned in previous units. The resources include handout describing the task, detailed rubrics outlining how to get the points, and a rubric grading sheet for each small piece of the project as well as the final project.
General Rubric
Detailed Rubric
This year I am going to get the audience more involved. Three students will grade the students using this rubric. Then three other students will grade the solution of the problem using the AP rubric. I will also require students to ask one question during the course of the presentations. I wanted to make it more than one, but was not sure if I made it more that there would be time for all the students. I was going to check this off and put it in the grade book.
I will look at their feedback and check that they are doing it to give them a feedback grade that will go in the in-class category. I will check off who has asked a question and give them points for that in the in-class category.
I will average the scores given by the students using the AP rubric and put that score in the homework category.
I have also considered averaging the students scores on the presentations with mine.
So next year I will be teaching 5 periods of class a week instead of 6. So two days a week I will see a class for 90 minutes and one day a week I will see the class for 45 minutes. So during the 90 minutes I will teach one section of the textbook. So I will teach two sections of the textbook a week. Then on the day I have the students for 45 mins I will have the students take a short quiz. Then once they are done with the quiz they can work on their project. Depending on the schedule I will probably have them turn that weeks part of the project in at the end of the period.
So instead of homework I will have a weekly quiz. I am think the quiz will have five multiple choice questions on it and the students will have 15 minutes to answer the questions. That is the amount of time they will get on the AP test. The remaining class time I will check in with students on their projects and give them time to work on it. If a student is done I can let them get started on the next part. I will have to have the handouts ready far in advance though. I am planning to use AP questions on the quiz.
I made a rubric to grade students notes and taught the students how to take good notes this year. I wanted to grade and collect the notebooks a lot, but did not have time since I was spending it grading everything else. I have also learned that I can only grade one class set of notebooks in one week. So I think each week I will collect the notebooks of one class. That way I am grading and giving feedback on their notes every three weeks. I will talk about how I grade notebooks and what I have discovered so far this year in another post.
For the in-class portion of the grade I will grade any activities that are done in class. However next year I am planning on using an app called class dojo to monitor student behavior and participation. One of my colleagues here in China uses it with his classes. He gives points for things like critical thinking and takes away points for speaking Chinese. At the end of the six weeks he looks at the summary points and gives them the grade according to that. I have to decide what criteria I will be looking for. I will also have to make sure I can use the app in the classroom since their is no wifi and the internet. I know it can be done, but I will have to test it out before I use it next year.
Here is my criteria:
Positive:
Different solution method
Critical thinking
Questions
Helps others
Negative:
Unprepared
Speaking in Chinese
Off task
I want to make these categories meaningful. I am try to think about what behavior in class makes a good math student. I would love more suggestions of categories to add.
I will try to keep you updated on how using class dojo impacts my classroom.
Thursday, December 1, 2011
Campus Photos
So I thought you guys would like to see more of the campus. So here are some photos from around the campus.
Here is the view of the school when you walk in the front gate. They are some great panorama photos.
The brick building on the far left is the buiding I teach in and where the AP center is.
The building in the middle with the halo ring is the information building. It has the library, auditorium, and the music classes are held there. Glee club meets on the 6th floor in the choir room. The IT department is also located in this building. I am told it is mostly empty though. I have not really explored though. I want to see the library though. I am told it is pretty empty and does not have many research books. None of the students use it anyways.
The brick buildings at the right are more classroom buildings I believe.
That white building on the far right I believe is ours and empty. The principal says they are going to tear it down and that will be our new building. Right now the TAG middle school kids are on the first and second floor of our building. We have classes and offices on the third and fourth floor of our building. So we have been promised our own building to ourselves.
This is another statue on campus. It is located near the building I teach in. This is called a ding and many were made in Ancient China. The Chinese staff were surprised that I knew the name of the statue. However I studied these and other types of common artifacts from Ancient China in the art history class I took that focused on the art of China. When I saw it I fell in love with it and was like oh look it is a ding. I got strange looks I think. I had to wait to take pictures of it though. The bamboo was growing everywhere and at the beginning of school they were on trimming it all back.
Here are the roses that grow in the garden area next to the building I teach in. At first when they were not in bloom they were quite ugly. However the first time I saw them in bloom it was calming. We usually walk through this garden area on our leisurely stroll back from the cafeteria after lunch. I hope the photo bugs are ok with my close up of the rose. I felt like my Dad or sister would have done it better or spent more time getting the right picture. I just took a quick shot.
Now here is a panoramic view of the lake from inside the pagoda. You can see the information building with the halo on top. You can see the dorm buildings across the way. The brick buildings on the far right of the second photo are the staff dorms.
So that is more views and sites from around Tianyi campus. I hope you all enjoyed seeing where I work. I am told the campus is even more beautiful in Spring. So I will have to post more photos when spring comes.
Here is the view of the school when you walk in the front gate. They are some great panorama photos.
The building in the middle with the halo ring is the information building. It has the library, auditorium, and the music classes are held there. Glee club meets on the 6th floor in the choir room. The IT department is also located in this building. I am told it is mostly empty though. I have not really explored though. I want to see the library though. I am told it is pretty empty and does not have many research books. None of the students use it anyways.
The brick buildings at the right are more classroom buildings I believe.
That white building on the far right I believe is ours and empty. The principal says they are going to tear it down and that will be our new building. Right now the TAG middle school kids are on the first and second floor of our building. We have classes and offices on the third and fourth floor of our building. So we have been promised our own building to ourselves.
This golden apple is a statue that you couldn't see in the panorama. I think the golden apple is supposed to represent wisdom and the color gold is supposed to be one of the best. You can see the fountain behind the golden apple. Then I included a close up of the fountain. It is only turned on one day of the year and that is open house day. I didn't get a picture of it because I was busy prepping for the big open house day lesson.
I will try to get a picture of it next year.
So this is the bridge around the lake on the far side of the lake behind the information building. This is where I took my school photo that you may have already seen. You see some of the lake and the area around it. The brick buildings in the back are teacher and staff dorms. The tall buildings in the very back are apartment buildings in the apartment complex I live in.
So these are panorama shots of the school around the lake. You can see the information building in this picture in the forefront of this picture on the very left. Across the lake is the cafeteria and the building I work in. The students dorms are also in the very back of this photo on the far side of the lake.
This is the pagoda on the side of the lake. They started building this at the beginning of the year. It was done sometime in October. We came back from our one week holiday and it was suddenly done. It didn't seem like it was going to get done that quickly. I think it is a very pretty addition though.
Now here is a panoramic view of the lake from inside the pagoda. You can see the information building with the halo on top. You can see the dorm buildings across the way. The brick buildings on the far right of the second photo are the staff dorms.
So that is more views and sites from around Tianyi campus. I hope you all enjoyed seeing where I work. I am told the campus is even more beautiful in Spring. So I will have to post more photos when spring comes.
Friday, November 18, 2011
Math is a Universal Language
So a while back each of the foreign teachers met with the Chinese teachers in their subject. So I talked with the Chinese math teacher. Since I only teach grade 11 or juniors I talked with the 11th grade math teacher. So we talked about limits and being clear for the AP test. He asked about the definition of limits. I showed him my textbook that had the definition using delta and epsilons. I told him that they did not need to know that for the AP test. So we were having a good conversation. Then I asked him what he taught. He teaches them the math on the SAT II test. So this semester they are preparing for the SAT II math test and then next semester the Chinese teacher will help them review for the AP test. I find it really weird that they take the SAT II subject tests because no one in America takes them. Everyone just takes the SAT I.
I asked him what he covered so I could understand the background and foundation before Calculus. He often couldn't understand the english words I pointed to. However when I showed him equations or symbols he understood. I think that is part of the beauty of math that it is a universal language. I had a lot of my conversation with graphs, equations, symbols, and hand gestures. I had a translator too, but I was happy to communicate using math. It was amazing to see. I just hope we can have more productive conversations about Calculus as the year goes on.
There was a photographer at the meeting that took a picture of me speaking with the math teacher. It was put on the billboards in front of the school. It was kind of cool to see my photo up there. There is also a general photo of me with my name and what I teach up on the school billboards. I just wanted to show you the pictures of the math meeting and cross cultural communication:
That is me, one of our Chinese staff to translate, and the 11th grade math teacher. I have all of my calculus textbooks out in front of me and my syllabus.
The other math teacher works with the 10th graders and 11th graders was talking with the other Chinese math teachers. I think he had a much more productive meeting than I did.
I think we are going to have another meeting with the Chinese math teachers. That should be very interesting.
I asked him what he covered so I could understand the background and foundation before Calculus. He often couldn't understand the english words I pointed to. However when I showed him equations or symbols he understood. I think that is part of the beauty of math that it is a universal language. I had a lot of my conversation with graphs, equations, symbols, and hand gestures. I had a translator too, but I was happy to communicate using math. It was amazing to see. I just hope we can have more productive conversations about Calculus as the year goes on.
There was a photographer at the meeting that took a picture of me speaking with the math teacher. It was put on the billboards in front of the school. It was kind of cool to see my photo up there. There is also a general photo of me with my name and what I teach up on the school billboards. I just wanted to show you the pictures of the math meeting and cross cultural communication:
The other math teacher works with the 10th graders and 11th graders was talking with the other Chinese math teachers. I think he had a much more productive meeting than I did.
I think we are going to have another meeting with the Chinese math teachers. That should be very interesting.
Wednesday, November 16, 2011
Tour of Tianyi
So I finally stopped and let myself gawk at the school campus. I took these photos on my walk home after school. There are still other places around campus that I want to take photos of to share with everyone. However here are the first few.
This is of a pagoda that is built on the side of the lake on campus. Yes I just said lake on campus. It has beautiful Koi fish in it. We stop on this bridge to feed them banana peels after lunch. The pagoda was built super quickly. It surprised me like crazy. It was just suddenly finished and built.
The large angular building in the back is the sports stadium and the gym. The gym is not finished. Next to that is supposed to be an indoor pool. We were told that it was going to be done at the end of September, but nope. I am looking forward to it getting finished though. I am hoping I can swim in the pool when it is done.
Here is a panorama of the area so you can see what surrounds the lake:
The above picture shows the bridge with the canteen/cafeteria in the far left corner. I think that is the gym or something in the far background.
Here is a panorama of the of the other side of the lake:
So there is he lake and surrounding buildings. I think that is the Information building in the far right corner. The information building is mostly empty from what I have been told. There is a library which is mostly empty as well. I have not seen it, but that is what I am told. I hope this gives you an idea of the area around the lake.
There is a beautiful rose garden near by our building that I want to show you guys. There are a few other important landmarks around campus that are worth seeing too. There are tons of fountains that only run on open house day. I did not get a chance to get out of the classroom to see them or take photos of them. I was too focused on making sure my dog and pony show of a lesson went well. Anyways that is a look at the school and I will share more of it later.
This is of a pagoda that is built on the side of the lake on campus. Yes I just said lake on campus. It has beautiful Koi fish in it. We stop on this bridge to feed them banana peels after lunch. The pagoda was built super quickly. It surprised me like crazy. It was just suddenly finished and built.
The large angular building in the back is the sports stadium and the gym. The gym is not finished. Next to that is supposed to be an indoor pool. We were told that it was going to be done at the end of September, but nope. I am looking forward to it getting finished though. I am hoping I can swim in the pool when it is done.
Here is a panorama of the area so you can see what surrounds the lake:
Here is a panorama of the of the other side of the lake:
So there is he lake and surrounding buildings. I think that is the Information building in the far right corner. The information building is mostly empty from what I have been told. There is a library which is mostly empty as well. I have not seen it, but that is what I am told. I hope this gives you an idea of the area around the lake.
There is a beautiful rose garden near by our building that I want to show you guys. There are a few other important landmarks around campus that are worth seeing too. There are tons of fountains that only run on open house day. I did not get a chance to get out of the classroom to see them or take photos of them. I was too focused on making sure my dog and pony show of a lesson went well. Anyways that is a look at the school and I will share more of it later.
Monday, November 14, 2011
A Teaching Victory
So as some of you may know I have been struggling with teaching so far. Your first year teaching is difficult because it is often the first time you are teaching the topics. It is tough managing the course load, grading load, and finding your presence in the classroom. It also takes you longer to plan such a good lesson. After more years of experience you know what activities work and you have lots of good teaching strategies.
So for me it is really tough because I am teaching Calculus. I never thought of teaching it. I am much more rusty with Calculus. I don't have good Calculus role models to mimic. I had horrible professors in college. I drew a lot of what I think a good teacher is from my Algebra and geometry teachers. So I have been struggling to keep up with planning, grading, and actually knowing the subject. The students expect me to be super on top of my game and all my bosses do too. The students I have ask some of the most challenging questions. They also will remember if you didn't answer one of their questions and will keep reminding you.
So I have been trying to bring in group work more and more. I have been working on incorporating that. It was going ok. I kept trying to rethink how to do group work and what questions to use. I kept trying to think of ways to get everyone talking. I was doing decent, but I had to be doing better.
I went to a workshop on highly effective teaching practices. We spent one morning preparing a lesson plan. I used this lesson plan today and the person who led the workshop came to see how I implement this lesson plan. So this what I did today and what went well.
So today I introduced how to do the chain rule.
I started with students looking at a graph of the function sin(x^2 - 4). I had this graph projected under the document camera. I gave the students 4 minutes to write down any observations about the graph. I timed them and kept them to 4 minutes. I then had them lift up their white boards and asked a few students to talk more about what they wrote. I talked over with the head of the math department about this. I should have had students come up and put their white boards under the document camera to extend the discussion. However what I was looking for was talking about the period, oscillation, and if it was symmetric. The graph gets as one student more and more dense because it oscillates more. This later translates to the graph of the derivative having a bigger and bigger slope. I then handed out a hard copy version of the graph for students to attempt to graph the derivative function. This was to get them to think about the derivative. I gave them five minutes to do this which was appropriate and I stuck to this time limit. I also gave them time warnings. Some saw that the graph of the derivative got a more and more positive slope. I got students who finished early to explain the graphing process to other students. I then projected the derivative graph to show them what they should have gotten. They are some crazy graphs. You should take a look. If you then look at the derivative function it turns out the original function is not symmetric (although looks very much like it). So this was the intro into the chain rule. So this lead amazingly into the objective for today which was to find this derivative algebraically.
So this led into talking about looking at the two equations and seeing that the derivative function is made up of two derivatives of which we already know. This lead into the objective beautifully because the objective was that students would be able to find the derivative using the chain rule. I wrote this up on the board.
So know that students have sort discovered or observed what the chain rule is. I introduced the theory and went over the theorem. I connected it back to the example in the beginning of class. Now I should have gone slower and provided one more example.
After this theory and explanation of the example. I had students work on three different problems. I chose increasingly harder problems. The first one was similar to the first example. The next was (3x^2 + 1)^2. This one was a little different and they could solve it using the old way. The last one required the use of the chain rule a couple of times. I gave the first one to the group of mostly weaker students. Then I gave the second one to some of my better students. Then I gave the last one to some of my better students. If a student solved the problem within the five minutes I told them to explain it to the other students around them. I then gave them another five minutes to solve the other problems. If one student solved the problem I encouraged them to explain it to the other students. Then near the end of the three minutes I asked students if they would present their answer. The first student was good. The second student made a mistake and I handled directing him to the right answer fantastically. He stayed to try and figure out the problem through the break. I then had the third student present the last problem. I was really proud of her because she struggled at getting this last problem. A few students were talking at the beginning of class and I quieted them. They still were talking so I went into the class and stood next to them. That sent the right message. So I was on my teaching game today. Now I just got to keep it up.
Then I had students fill out an exit slip. I asked them to write about one thing they learned today. However the more fun question was having students come up with the example that uses the chain rule and to solve it. I told them to get real creative and think of one that might use the chain rule more than once. There were some amazing answers. Some students were just laughing at how difficult they made the problem. I was so excited and the students enjoyed the chance to be creative. I think I will show some of these examples at the beginning of class. I could not do it during class because I had to move on.
I brought in four different Free response questions over the material we had covered so far. I gave students three minutes to solve the problem. This was not enough time to solve the problem. Then when they had to rotate they had to read the work from the person before them and add to it. We did this a few times so that each student saw each problem. Then they will have to present a problem they have not seen before in class next time.
This was good on paper, but I didn't think the groups or the problems enough. The rotation did not work out and not all of the students saw each problem. So I realized how my math was off and I am changing the structure some for tomorrow.
There was also this funny movement where I was going to make all of the students move about the room to each problem. The students did not like this idea and one girl raised her hand to ask why the papers couldn't switch from group to group. I laughed it off and said well I thought we could get some exercise in Calculus and thought you would like that exercise in Calculus. They laughed at the joke and I said sure we can make the questions move if you don't want your exercise. I was debating over these two structures and though moving would be more fun.
Tomorrow I will be getting the students in groups of four. Each student in the group will get a different question. Then they will rotate questions after three minutes. I will do four rotations so each student sees each problem. Each student will have to add on to the previous students work. Then at the end the group will work together to present one of the four problems. Then now that they have seen each one they can help work on the presentation.
The students were engaged through out the lessons. They had fun and I had fun. They laughed at my jokes. I made the lesson personal by throwing in a few comments.
I had also planned for students to work on a challenge question, but I cut it because it was more important for the students to present answers and work on the exit slips and free response questions. It was a great choice.
So I handled the classroom management very well. I made good teaching decisions. I handled the teaching moments very well. I kept students moving by keeping them to strict time limits. I had a problem with this earlier. I used an online clock timer. It is a portable app that you can install on your USB stick (portable timer app). It is a great visual for you as a teacher and for the students. I have it counting down on the computer and have the projector displaying the computer screen. At the end if you have the volume on then it will give a buzz sound. If the students are really engaged then this jumps them right out of it and tells them it is time to move on. I still have areas to improve on. However today was a great lesson.
I had students missing today because they are on a habitat for humanity trip and I hope the classroom dynamics do not change when they come back. Today was great and dynamics were great, so hopefully it stays the same. The students who were missing I think are instigators of immaturity. It will be interesting indeed.
Overall the lesson went well. It will be absolutely excellent tomorrow. I left feeling great. I felt even great when the head of the math department reinforced this thought. She caught moments that I made good choices and decisions that I sort of just did instinctively. I want to parlay this great lesson into more great lessons. I will use this structure and activities to set up other lessons. It was lessons and days like that remind me why I want to teach. This is what I always dreamed my classroom to look like. Now did I imagine it in Calculus or in China, No I didn't. However I did picture stimulating students and making them think. I did imagine letting students be creative. I did imagine having students discussing how to solve problems together.
Earlier in the year I wanted to cry because I was just so overwhelmed with everything. I left today wanting to cry tears of joy. I felt like I had finally done in the classroom what I always dreamed of and I enjoyed it. I had lots of fun. I love this feeling too much not to have it happen again.
So for me it is really tough because I am teaching Calculus. I never thought of teaching it. I am much more rusty with Calculus. I don't have good Calculus role models to mimic. I had horrible professors in college. I drew a lot of what I think a good teacher is from my Algebra and geometry teachers. So I have been struggling to keep up with planning, grading, and actually knowing the subject. The students expect me to be super on top of my game and all my bosses do too. The students I have ask some of the most challenging questions. They also will remember if you didn't answer one of their questions and will keep reminding you.
So I have been trying to bring in group work more and more. I have been working on incorporating that. It was going ok. I kept trying to rethink how to do group work and what questions to use. I kept trying to think of ways to get everyone talking. I was doing decent, but I had to be doing better.
I went to a workshop on highly effective teaching practices. We spent one morning preparing a lesson plan. I used this lesson plan today and the person who led the workshop came to see how I implement this lesson plan. So this what I did today and what went well.
So today I introduced how to do the chain rule.
I started with students looking at a graph of the function sin(x^2 - 4). I had this graph projected under the document camera. I gave the students 4 minutes to write down any observations about the graph. I timed them and kept them to 4 minutes. I then had them lift up their white boards and asked a few students to talk more about what they wrote. I talked over with the head of the math department about this. I should have had students come up and put their white boards under the document camera to extend the discussion. However what I was looking for was talking about the period, oscillation, and if it was symmetric. The graph gets as one student more and more dense because it oscillates more. This later translates to the graph of the derivative having a bigger and bigger slope. I then handed out a hard copy version of the graph for students to attempt to graph the derivative function. This was to get them to think about the derivative. I gave them five minutes to do this which was appropriate and I stuck to this time limit. I also gave them time warnings. Some saw that the graph of the derivative got a more and more positive slope. I got students who finished early to explain the graphing process to other students. I then projected the derivative graph to show them what they should have gotten. They are some crazy graphs. You should take a look. If you then look at the derivative function it turns out the original function is not symmetric (although looks very much like it). So this was the intro into the chain rule. So this lead amazingly into the objective for today which was to find this derivative algebraically.
So this led into talking about looking at the two equations and seeing that the derivative function is made up of two derivatives of which we already know. This lead into the objective beautifully because the objective was that students would be able to find the derivative using the chain rule. I wrote this up on the board.
So know that students have sort discovered or observed what the chain rule is. I introduced the theory and went over the theorem. I connected it back to the example in the beginning of class. Now I should have gone slower and provided one more example.
After this theory and explanation of the example. I had students work on three different problems. I chose increasingly harder problems. The first one was similar to the first example. The next was (3x^2 + 1)^2. This one was a little different and they could solve it using the old way. The last one required the use of the chain rule a couple of times. I gave the first one to the group of mostly weaker students. Then I gave the second one to some of my better students. Then I gave the last one to some of my better students. If a student solved the problem within the five minutes I told them to explain it to the other students around them. I then gave them another five minutes to solve the other problems. If one student solved the problem I encouraged them to explain it to the other students. Then near the end of the three minutes I asked students if they would present their answer. The first student was good. The second student made a mistake and I handled directing him to the right answer fantastically. He stayed to try and figure out the problem through the break. I then had the third student present the last problem. I was really proud of her because she struggled at getting this last problem. A few students were talking at the beginning of class and I quieted them. They still were talking so I went into the class and stood next to them. That sent the right message. So I was on my teaching game today. Now I just got to keep it up.
Then I had students fill out an exit slip. I asked them to write about one thing they learned today. However the more fun question was having students come up with the example that uses the chain rule and to solve it. I told them to get real creative and think of one that might use the chain rule more than once. There were some amazing answers. Some students were just laughing at how difficult they made the problem. I was so excited and the students enjoyed the chance to be creative. I think I will show some of these examples at the beginning of class. I could not do it during class because I had to move on.
I brought in four different Free response questions over the material we had covered so far. I gave students three minutes to solve the problem. This was not enough time to solve the problem. Then when they had to rotate they had to read the work from the person before them and add to it. We did this a few times so that each student saw each problem. Then they will have to present a problem they have not seen before in class next time.
This was good on paper, but I didn't think the groups or the problems enough. The rotation did not work out and not all of the students saw each problem. So I realized how my math was off and I am changing the structure some for tomorrow.
There was also this funny movement where I was going to make all of the students move about the room to each problem. The students did not like this idea and one girl raised her hand to ask why the papers couldn't switch from group to group. I laughed it off and said well I thought we could get some exercise in Calculus and thought you would like that exercise in Calculus. They laughed at the joke and I said sure we can make the questions move if you don't want your exercise. I was debating over these two structures and though moving would be more fun.
Tomorrow I will be getting the students in groups of four. Each student in the group will get a different question. Then they will rotate questions after three minutes. I will do four rotations so each student sees each problem. Each student will have to add on to the previous students work. Then at the end the group will work together to present one of the four problems. Then now that they have seen each one they can help work on the presentation.
The students were engaged through out the lessons. They had fun and I had fun. They laughed at my jokes. I made the lesson personal by throwing in a few comments.
I had also planned for students to work on a challenge question, but I cut it because it was more important for the students to present answers and work on the exit slips and free response questions. It was a great choice.
So I handled the classroom management very well. I made good teaching decisions. I handled the teaching moments very well. I kept students moving by keeping them to strict time limits. I had a problem with this earlier. I used an online clock timer. It is a portable app that you can install on your USB stick (portable timer app). It is a great visual for you as a teacher and for the students. I have it counting down on the computer and have the projector displaying the computer screen. At the end if you have the volume on then it will give a buzz sound. If the students are really engaged then this jumps them right out of it and tells them it is time to move on. I still have areas to improve on. However today was a great lesson.
I had students missing today because they are on a habitat for humanity trip and I hope the classroom dynamics do not change when they come back. Today was great and dynamics were great, so hopefully it stays the same. The students who were missing I think are instigators of immaturity. It will be interesting indeed.
Overall the lesson went well. It will be absolutely excellent tomorrow. I left feeling great. I felt even great when the head of the math department reinforced this thought. She caught moments that I made good choices and decisions that I sort of just did instinctively. I want to parlay this great lesson into more great lessons. I will use this structure and activities to set up other lessons. It was lessons and days like that remind me why I want to teach. This is what I always dreamed my classroom to look like. Now did I imagine it in Calculus or in China, No I didn't. However I did picture stimulating students and making them think. I did imagine letting students be creative. I did imagine having students discussing how to solve problems together.
Earlier in the year I wanted to cry because I was just so overwhelmed with everything. I left today wanting to cry tears of joy. I felt like I had finally done in the classroom what I always dreamed of and I enjoyed it. I had lots of fun. I love this feeling too much not to have it happen again.
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