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.

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. 

Project 1: General Properties of a Function

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 3: Fundamental Theorem of Calculus

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.

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. 

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.