## Sunday, 17 November 2013

### Calculus Activity: Rolling Ball in an Inclined Plane

The second lab activity we did in our AP Calculus AB class was to find the optimal angle for the inclined plane to get the maximum distance on a ball that is rolling from the inclined plane. Below is the activity instructions.

Determine the ideal angle of an inclined plane in order for a ball to roll the furthest

Material: Inclined plane (using two meter ruler), tennis ball, protractor, measuring tape

1. Decide on a “starting point” along the inclined plane that you will use.
2. Choose different angles for the inclined plane, drop the ball from the “starting point” and let the it roll down and along the corridor.
3. Record the angle of the inclined plane and the distance the ball rolled. (You might want to take more than one measure for each angle and take the mean). You can choose as many or as few different angles as you think relevant, but don’t forget to choose a range that include “extreme” angles.
4. Using your data, create a scatterplot on your calculator and find a model for the distance the ball rolls in terms of the angle.
5. Algebraically determine the ideal angle in order to have the ball roll as far as possible.
6. Check whether the model works or not.
7. Draw conclusions on what you have seen, calculated and discovered.

In the past, I have asked students to submit a lab report on the activity, but this year, as we are building on the iBook for our learning portfolios, they will be submitting their work as a chapter in their iBook.

Below is a quick video of students performing the activity.

## Thursday, 7 November 2013

### Summative Assessment: Testing for Mastery vs Snapshot of Understanding

As educators, we have varying opinions with regards to student assessments. I myself was a teacher that was very one dimensional when it came to assessments. I felt as a math teacher, there really wasn’t much that could be done for summative assessment except for quizzes and tests. That they had to be a snapshot of understanding in order for the grades to reflect their true ability and if they performed badly, perhaps students would use it as a motivating factor to do better in the next unit. I realised how wrong it was for me to think this way. I am an educator. My goal shouldn’t be to trick students into learning, rather to motivate them to want to improve themselves one day to the next. I used to tell my students “Grades are not important as long as you are improving your understanding and skills and learning from your mistakes.” I say that, but was I really providing the opportunity for that growth? How am I motivating them to learn if they continually feel defeated by their scores? It was time for change.

Our students are not a homogeneous group and have different rates of learning. I wanted to create a system where students take an assessment, be allowed to go back, re-learn/practice concepts they have missed and come back to take the assessment again (of course, a different version of the assessment that tests the same knowledge/skills) to show that they have mastered it. Although it is a summative assessment, it is more formative in nature. This way, we are targeting different skills that students lack and give them multiple opportunities to demonstrate mastery in those skills. But you may ask, to be able to do this, it requires time. Time that we don’t often have to spare in certain classes. I do admit that it is easier to implement such system in a flipped classroom. (Clickfor my blog post on developing materials for a Flipped Classroom. Clickfor my blog post on how I structure my class time in my Flipped Classroom.)

When making changes to our teaching practices, it is often unrealistic to apply the changes to all our classes at once. So, I used my experimental Student-Led Project Based Learning class to see how I can promote mastery in their learning. (Clickfor the full blog post about my experimental class.) My goal was to allow students multiple attempts at a same skilled assessment until they have mastered it. So I gave them three different opportunities to take the assessment and to improve on it each time. This worked well in theory, but I did run into some obstacles. 1) We have a testing policy in our school, so any summative assessments have to be given at a specific time slot, which means there was limited flexibility in when these assessments could be given, 2) because I work at a school that students are highly stressed, students were not taking the opportunity of the multiple assessment and many of them just took the last one offered, which goes against this whole theory.
Having learned from that, I have now required students to take the assessment a minimum two times and I have included some “Problem Solving Bootcamp” days into the schedule where we all, as a whole class go through a bunch of questions together.

Ideally, I would love to see students be given as many opportunities as they need to demonstrate their mastery. And if it takes many months to master one skill, wouldn’t that be better than moving on without mastering it at all? I know in our current education system this is not easy. However, I do believe it is important for us, as educators, to talk about our assessment practices and to question what purpose our assessments are serving for our students.