Calculus and Kobe Bryant

I used this video in my calculus class to show how math can either support or disprove a movie.

I showed this movie to my students and asked if this looked possible.  One jumped up and said "No way!" while others thought it could happen.  What was interesting was when I asked "Do you have proof?", as the class went silent. 

The math in this movie is incredible. 

Where I thought the students would go was completely the opposite of what happened.  My students timed how long Kobe was in the air, we measured his height in the movie and compared it to his real height to create a scale.  We used integration using gravitational pull to be -9.81m/s^2, to create a velocity and distance function.  The calculus was amazing. 

Whether we proved or disproved the reality is a secret I keep with me as I challenge you to give this to your students and see what they do.  Just watch the movie then ask "Any questions?"  I bet you will get lots.  The secret is then to let them "play" with the math and the movie.

Learning is road that they must travel down themselves and we should only be guiding them not pulling them along by the hand.

Awesome Education Talk in Red Deer

Yong Zhao is coming to Red Deer Wednesday February 8.
Tickets are $10 and are donated to the Red Deer Women's Shelter.

Amazing speaker for parents, future and current educators and as well as anyone interested in Education.

More information, and how to buy a ticket can be found here

Students create the problem to solve

Math 31 Assessment

Option 1: The head of NASA has approached you asking for your assistance plotting a course for the International Space Station.  The tracking device can be found at http://spaceflight.nasa.gov/realdata/tracking/index.html .  NASA needs an equation of the path, as well as the 1^st and 2^nd derivative.  The director is also asking for all relevant information about the path to be explained.  Create a potential problem the satellite might encounter and provide the solution to the problem.

Option 2: Ethan Hunt, an IMF point man, is securing top secret files at the bottom a cylindrical tube.  He is being lowered by rope into the room at a constant speed.  Unfortunately, while being lowered, another man walks, at a constant rate, towards the room.  Ethan is then raised back up out of the view of the approaching man.  While suspended in air, sweat is building at a constant rate until it reaches a critical value and drops onto the floor.  Using the video (a clip can be found here http://www.youtube.com/watch?v=k-oVuQpjG3s) use calculus to help out Ethan and determine various velocities, critical values, and timing to assist him in securing the evidence.

Option 3: Taking what you’ve learned this semester you must create a problem to solve. It must be based on a real world example (or movie world) and must have at least one solution. Be sure to submit your proposed solution in a sealed envelope. Five bonus points will be awarded if you are able to stump your teacher.

No matter which option you choose you must create the question and problem in the given scenario

	Calculus Student	Calculus Student Teacher	Calculus Teacher	Calculus Master
Real Life Application: Is the problem worthwhile solving? What are the implications of the result of the problem? Who would benefit with the knowledge of the answer to your problem?	Only students of this course would see the relevance of this problem. The purpose is built on strictly recalling facts. The solution is only needed to complete this assignment.	Problem is created from a plausible issue with major changes. Purpose is unclear and does not go beyond the needs of the course. Students in this course would only understand the consequences of the solution to the problem.	The problem is created from a plausible issue or problem with minor changes. The purpose is clear and slightly exceeds the needs of this course. Few, outside this course, would benefit from the solution to the problem.	The problem is created from a real life issue or problem. The purpose is meaningful beyond the needs of the course. The solution to this problem adds to the experience of the students’ real world knowledge.
Explanation of math. Are you using basic math knowledge? Are you demonstrating most of the knowledge you learned in this course?	Focuses strictly on basic recall and basic knowledge of the mathematical skills.	Requires few sections to apply higher level thinking to solve the problem. Math is still largely focused on recall of knowledge.	All levels of understanding, from basic to higher level thinking are implemented throughout the problem.	Focuses on higher level comprehension, the use of the combination of multiple skills is evident throughout the entire solution.
Communication of your answer: Does your work follow sequentially throughout your solution? Are there gaps in your communication?	Minimal response is given with multiple gaps in the explanation process.	The use of similar explanation techniques is used throughout the solution.  Communication is limited with various gaps in the problem solving.	Most of the project is easily understood, and organization is mostly logical.	The use of different means of demonstration is illustrated throughout the solution.  The mathematics is clearly communicated as well as the meaning of the solution(s)

Discussion with a first year teacher around marks

Recently, I had a discussion with a first year teacher after 4 months of teaching in her first year, here is how it went:

Her: I’m scared I not going to have enough summative assessments at the end of this year.

Me: How many is enough?

Her: I went around to other teachers and discussed and the general consensus is around 25-30 if I averaged it out.  Some teachers had even given 50.

Me: Do these other teachers teach the same exact students you do?

Her: No, they teach different courses and different subject

Me:  How do the students of other classes and teachers of different subjects have anything to do with your students?

Her: Then who should I be asking?

Me: your students, ask them how important is having 30 assessments, would you prefer less assessment of higher quality or more of lower quality?  We must understand that the more grades we give students, the more we lower the value of everything we have graded to far.

her: Dave, don’t we give more summative assessments to allow for students to have more chances in achieving the best grade possible.

Me: So it sounds as if this strategy has nothing to do with learning.  It sounds as if we are giving more assessments to allow students to get the best score in the “Game” of school.

We then engaged in a discussion around the meaning of assessment and marks.  She started from a belief that there is an actual number of summative assessments which she is required to have for each student.  I hope I showed how wrong this belief was!  Teachers never should have a goal of the number of summative assessments to give students, and in fact we should be aspiring to have zero summative assessments throughout the course and start moving to entirely formative assessments.  The only summative assessment which should occur is at the end of the course, only under the assumption that no more learning can occur.

Facts and Myths of traditional learning in schools

It is little short of a miracle that modern methods of instructions have not completely strangled the holy curiosity of inquiry – Albert Einstein

From “Breaking Free from myths about teaching and learning” by Allison Zmuda, we learn about various myths and facts about learning in the traditional classroom, and my synopsis:

Myth: The rules of this classroom and subject area are determined by each teacher:

This is false as the push for meeting provincial (and state) standards increase, the autonomy of the individual teacher decreases.  Collaboration is being used to enforce compliance as well as standardizing the rules of each classroom.  For learning to be meaningful it must stem from personal experiences, current issues from students, as well as address the personal attributes of each student.  This cannot be achieved by blanket policies which affect all.

Fact: What the teacher wants me to say is more important than what I want to say:

This is truly a sad fact about our education system.  It is entirely summed up by a student who said:

It’s easy to take what the teacher says and regurgitate it without even thinking about what was said, and it’s how we’ve been taught to learn.  When I set out to write a paragraph, I actually thought I should ask my teacher to spell out what he wanted me to write… If I tried to challenge my teacher, all it would take is a little bit of him pushing back to make me drop my argument and look like a deer in the headlights, even if I had a decent argument.  Now that I know how passive I’ve been, I’m ready to make some changes in my learning style.

 Students need to have opinions in classes, and the teachers need to be cognisant of these ideas.

Fact: The point of an assignment is to get it done so that it’s off the to-do list:

In our schools, too many students are feeling overwhelmed to get the assigned readings complete, answer the repetitive math questions, study for the Biology exam and still have time to pursue to their own interests outside of school.  One student has even said

Most students just do the assignment because there is not time to really study it.  We don’t really get a chance to go further into the parts of the topic we are studying that aren’t part of the curriculum because we have already moved to a whole new topic.

We, as educators, must be aware that for students to complete all their “homework” they must take shortcuts and thus truly never understand the material at a deeper level.

Myth: I feel proud of myself only if I receive a good grade:

Students are using grades to truly sort themselves among their friends and classmates.  I believe all teachers have heard comments such as:

I got an F on this exam, but that is ok because I am not good at it.

I got a B like I always do, so I am doing fine.

No one is getting an A, so makes sense that I am not getting one either.

Grades and other extrinsic rewards are actually limiting the potential success of students.  Students are actually seeing the grade as an indicator as to how well they are playing the game of school.  As we push for improving learning we must move away from using grades to motivate students.  Students are proud of the product of their education not the mark they receive on how well they have manipulated their education

Myth: Speed is synonymous with intelligence:

Too many times we are pushing students to complete tasks at a speed which is unnatural to their own learning.  We are stripping education of passion and interest and replacing it with efficiency.  This can be seen in math classes when we teach “math tricks” and justify it by “this is the fastest way to get to the answer”.  Other educators validate this idea of rushing to complete the course due to the amount of material that is needed to be covered in a short amount of time.  The pressure to prepare students for standardized exams and complete the overwhelming curriculum is making it quite difficult for teachers to accept alternate views of learning, instruction using discovery methods, and taking time to allow for each student to deeply understand a topic before moving on.

More myths and facts exist, and I encourage all to read the book…WOW!

In the teaching to which I aspire to

I would truly allow each student to be an individual. To allow students to guide, not only their learning, but as well as their assessment. Students will no longer be "passengers on a fast bus down a lone highway" but instead "participants on a field trip to a field of their choosing" .  Top down mandated policies focused on increasing test scores would be replaced with guidelines, created by and with teachers, to allow for deeper learning. Teacher PD will always be encouraged as the work teachers do outside of school is just as important as the work they do inside the school.  

Outcomes will no longer be delivered in the hundreds, where each is extremely specific, but come in few general outcomes. This will allow for teacher autonomy in classes and allow for learning to be focused around the needs, wants, aspirations, and goals of each student instead of the goals of the system.

Technology, with unfilitered access, will be used in classrooms to create engagement around learning instead of being implemented to trick students in completing mundane tasks.  The goals of each class will be around meaningful questions instead of repeptive answers.

Teaching will be around one single absolute goal; lighting fires of interest and curiosity in each student of the school.