## ImagineIT - Phase Two

My school is on the north side of Chicago and consists of roughly 1,600 students. The classes I will be focusing on with this project are my two AP Calculus AB classes, both of which have a mixture of Juniors and Seniors. Each class meets for 50 minutes, four days a week, and for 49 minutes on Wednesdays. I may also incorporate this into my AP Calculus BC class, since the students makeup and content is similar.

The focus of my ImagineIT project will be Perseverance in Problem Solving. I have found that one of my biggest headaches, and one of the students’ biggest frustrations, has been (a) the inability to either finish a problem, due to various factors, or (b) the ability to actually start to solve a problem.

In doing research on grit and perseverance, it seems to me that there are two main issues students have with word problems. First is their inability to begin. Do they have the skills and abilities to solve a word problem? Most likely, yes, if they have been keeping up in class. But once they see a word problem, it seems like all of the tactics and theorems come rushing into their head and they cannot decide which strategy or theorem to apply. It’s almost as if they are paralyzed by choice.

The second issue is that of fear. Students are afraid of either making the wrong choice, or they are afraid that they cannot solve the problem, which leads to them not finishing the problem. This fear may stem from a lack of confidence in their ability; possibly a peer-related comparison, where they see themselves as much less intelligent than their peers; or a lack of ability to determine whether their answer is logically correct (e.g. getting an answer that a gallon of milk weighs 3 pounds versus weighing 25 pounds).

In terms of activities, I’d like to have students work with more problems that are missing information in them, so that they could determine what types of information they need while they read the problem, as opposed to trying some method that they’ve seen done and hoping it fits the solution.

Another activity I am going to implement is to flip the classroom for a majority of the year so that students have more time to explore and play with problems in a safe environment and allow their questions to be answered immediately, by either me (good) or a peer (better).

The performances of understanding I will be looking for will mainly include students taking a math concept and applying it to a real-world situation, and then presenting it to the class. It’s easy to see a theorem and apply it to an example when it looks just like the example, but much of the AP Calculus exam, and advanced math in general, is about knowing when a theorem should be applied, not just regurgitating it over and over again. I would also like to pair this with some engineering or science and have students produce a product of some sort. I may look back at old Moody’s Math Challenges for ideas. Finally, I would also like students to look back at historical disagreements in math and have students debate these ideas.

As I stated earlier, I would like to implement one main pedagogical approaches - the flipped classroom. I believe that this, coupled with relevant performances of understanding, especially when they address paralysis of choice and fear, will help students become better problems solvers. Technology will be used as an aid to help students learn, including the use of ELMO-like projectors to present ideas, the use of Mathematica in illustrating concepts, having videos available of concepts (flipped classrooms) and the use of social media to engage students in discussing concepts and communicating mathematically both inside and outside the classroom.

The focus of my ImagineIT project will be Perseverance in Problem Solving. I have found that one of my biggest headaches, and one of the students’ biggest frustrations, has been (a) the inability to either finish a problem, due to various factors, or (b) the ability to actually start to solve a problem.

In doing research on grit and perseverance, it seems to me that there are two main issues students have with word problems. First is their inability to begin. Do they have the skills and abilities to solve a word problem? Most likely, yes, if they have been keeping up in class. But once they see a word problem, it seems like all of the tactics and theorems come rushing into their head and they cannot decide which strategy or theorem to apply. It’s almost as if they are paralyzed by choice.

The second issue is that of fear. Students are afraid of either making the wrong choice, or they are afraid that they cannot solve the problem, which leads to them not finishing the problem. This fear may stem from a lack of confidence in their ability; possibly a peer-related comparison, where they see themselves as much less intelligent than their peers; or a lack of ability to determine whether their answer is logically correct (e.g. getting an answer that a gallon of milk weighs 3 pounds versus weighing 25 pounds).

In terms of activities, I’d like to have students work with more problems that are missing information in them, so that they could determine what types of information they need while they read the problem, as opposed to trying some method that they’ve seen done and hoping it fits the solution.

Another activity I am going to implement is to flip the classroom for a majority of the year so that students have more time to explore and play with problems in a safe environment and allow their questions to be answered immediately, by either me (good) or a peer (better).

The performances of understanding I will be looking for will mainly include students taking a math concept and applying it to a real-world situation, and then presenting it to the class. It’s easy to see a theorem and apply it to an example when it looks just like the example, but much of the AP Calculus exam, and advanced math in general, is about knowing when a theorem should be applied, not just regurgitating it over and over again. I would also like to pair this with some engineering or science and have students produce a product of some sort. I may look back at old Moody’s Math Challenges for ideas. Finally, I would also like students to look back at historical disagreements in math and have students debate these ideas.

As I stated earlier, I would like to implement one main pedagogical approaches - the flipped classroom. I believe that this, coupled with relevant performances of understanding, especially when they address paralysis of choice and fear, will help students become better problems solvers. Technology will be used as an aid to help students learn, including the use of ELMO-like projectors to present ideas, the use of Mathematica in illustrating concepts, having videos available of concepts (flipped classrooms) and the use of social media to engage students in discussing concepts and communicating mathematically both inside and outside the classroom.