I was recently involved in a session about creativity in the classroom.The presenter brought forth the fallacies with common and traditional assessment.After lots of discussion, case studies, videos, and examples of alternate assessment and instruction the session ended.
First off, I have to say that the staff that participated was amazing!The open minds, deep conversations and already exemplary teaching styles were quite evident.However, nothing made me more amazed than the comment the principal said at the end of the session.After the applause to the presenter, the thank yous and handshakes the principal stood up, looked at his staff and said:
“Imagine if you were driving down the highway in a brand new 2011 Mustang.The cops have all been called away from the road, the deer have been contained, and all other drivers are giving you the full road to explore and try out this new car”
“Ummm…ok” said a teacher in the crowd
The principal paused then started again
“Now let’s take this to a classroom.One day next week, let’s pretend there are no final exams, no unit tests, no marks to update, no mandated curriculum, and no one from Alberta Education to tell you what to teach.Take one day and let your students explore their own learning.Using the taught strategies in this session, open the “learning” doors for students and just let them discover something that as meaning to them”.
If hugging was socially acceptable I would have given this administrator the biggest one ever.Driving home, I thought of “What would schools look like if all administrators gave this chance to their teachers?What if every day was this special day?What if the needs of the students overpowered the needs to teach the curriculum?
I hope all his staff follow through with his directive and truly allow for authentic and autonomous learning to occur, if only for one day.
Awesome job Mr. Principal, I have found another individual who I would feel honored to call my boss!
Here is another example of how a student can do math without the use of a textbook or a worksheet.Many times I have, and will continue to, argue that math is not about repetition but actually deeper understanding.Also, in math class instead of learning about or for problem solving, we should be teaching students to learn through problem solving.
Problem solving is NOT completing a word problem at the end of a class, or using an algorithm to solve a problem.In the words of Andrew Wiles "The definition of a good mathematical problem is the mathematics it generates rather than the problem itself".Below, I will illustrate the 6 steps of implementing a well thought out problem solving activity in a class:
Step 1: Present an idea which students would want to solve.
Step 2: Have students ask the question
Step 3: Create a range of answers (students will feel safe to provide an answer)
Step 4: Provide any other information that a student may need to solve the problem....HOWEVER....have the students ask for the information.
Step 5: Allow for true autonomy to solve the problem.
Step 6: When students finish, or THINK they are finished, extend the thinking by giving a question that is not more of the same work, but entirely different solving.
Recently, in my calculus class, I showed the following video and gave a laptop to each student, with the video uploaded on it, to analyze it.Here is my lesson plan.
1)Watch the video.
2)I then asked the class, “Any questions about what we just watched?”(REMEMBER: We should get the students to ask the questions; there will then be no extrinsic rewards but only true intrinsic motivation to solve the problem.)
One student asked “How fast is the other car going?”
For which I responded, “Good question”
I then asked for the lowest possible speed of the car, and we determined that to be 109 km/h, while the upper bound for the speed would be 180 km/h.
As students worked they started to ask me for the length of my vehicle. Answering honestly, I informed them that I did not know this.They then followed my response with a question about the year and make of the vehicle I was driving, which was a 2011 GMC Terrain.
Students started to pull the actual length from the GMC website.
After several conversions, and 8 minutes of work, I took a picture of a student’s work and showed it on my projector.We then discussed alternate ideas, and where did this student have to estimate and where was he/she exact in calculations.
3) I then asked, “Is there anything else we could solve?”Again, another student asked, “What is the change of the distance between each driver as the car drives by?”
**Since I could not take an aerial photo of the situation, I did provide the students with a distance of 12 feet horizontally between the drivers**
Again, I asked the class to solve the problem.Within minutes, they realized they would need a specific time, and answered with “Solve for the instantaneous change of distance of the drivers after 3 seconds.”
After some solving, I took another picture and discussed the results with the class.
4) I asked the class if there still anything else we could solve. One student asked about the change in the angle of the arm that swung the camera. I responded with "Let's figure out the exact change in the angle at the time above".
This task took a little longer for some, while minutes for others. Those who did finish, or thought they finished early, I asked to calculate again but use a different method. By using a different method, they are applying a different strategy and also checking their answer at the same time.
We then did discuss various methods in the class.
Overall, I believe this lesson was a great success!!
Here are some pointers I have realized about true problem solving.
Never:
Tell the students they are correct or incorrect, ask if there is a way they could prove their answer another way.
Tell the students HOW to complete the problem, but instead ask them guiding questions.
Tell the students which way to solve the problem, but let them chose a method.
Do:
Scaffold for struggling students.
Answer questions, even if the answer is irrelevant to the problem.
Before, I used to teach finance in the following way:
Hand out a notes page, where the students would follow along and we would answer various questions. I would use charts, usually years old, and students would fill in answers I completed on the board.
This year, I took an extremely different approach. I handed out my finance project:
I no longer required my students to calculate the mortgage by hand, or by using a chart, but allowed them to determine the payment how most citizens would; using a program.
The students completed the project entirely using the Internet. By booking a computer lab, and bringing laptops into the class, students became extremely engaged in the project. After completing the sheet, they were required to create a presentation on their information.
Usually, when a student completes an assigned task they are assigned more of the same type of concept they just completed. (Which usually results in DRILL AND KILL). I took a different approach by assigning an entirely new task. When students completed the original task, I asked them to develop a budget for one month's spending, including their calculated mortgage payment.
The learning amazed me. In one instant, I had a student working on an excel sheet, which is a concept I plan on covering in two days. Other students were learning the difference between an open and closed mortgage; an outcome not required by the course.
Not once did I hear "When am I going to use this?" When students were having troubles they started researching all on their own. As I walked around the computer lab, I witnessed students on electricity websites, cell phone plans, cable companies, and other various utility websites.
Some students completed the extended tasks, and then analyzed if their "dream job" would cover their monthly expenses. Here are two of the presentations I received:
This year I gave my students an open-ended project. Below is a video that a student submitted. The project was entirely open-ended and when I assigned it I informed my students that it will be worth NO MARKS! Here is what I got from one student. (I will be uploading more but most are too large for YouTube).
Three students completed a 17 min video, another student completed an amazing powerpoint video, while a third group integrated calculus into a the world of Harry Potter. I truly was inspired when I witnessed the level of creativity and engagement completed by the students.
Was the motivation really from marks? Can't be that, as there were no marks. Maybe the motivation was from the chance to be autonomous and creative? I did not force my students to complete the project on a specfic outcome, nor did I force the tool they were to use to illustrate the outcome. All the task was "Show me something cool you have learned"
Here is the project that my department head created and I tweaked.
Math 31/35Multi-Media Project
To date you have covered several concepts within your math units.You now have the opportunity to use your other talents to share your knowledge with others via a multi-media presentation!
What kind of presentation?
That’s up to you….Powerpoint…video tape an interview with an expert… videotape yourself teaching a concept…videotape a skit showing mathematical instruction… a website.. a math lab…an everyday application of a learned concept…the possibilities are unlimited.
Some questions you might want your presentation to answer:
“When am I ever going to use this math?” and/or
“How could I help other students better understand a concept?”
Your presentation could focus on a single concept or on an entire unit
Do I have to do this on my own?
You can if you want, but that’s up to you.You can form a small group, I would suggest 3 or 4, but if you need more talk to me.Your group members can be from this class, any Math 31/35 class, or friends outside of class that have a talent that could add to your presentation.
What do I get out of this?
You gain an increased understanding and appreciation for mathematics.You would also be leaving a legacy behind here at the school, as I intend to use these projects to introduce and supplement unit material to future Math 31/35 students.
How do I get involved?
All you need to do is fill in the attached Project Proposal sheet and have all members of your group sign the release that allows me to use the material.Then let the fun begin!
What if I start it, but don’t finish, or if there are problems with the group?
Keep me informed on your progress.Whatever support or assistance you need I will try to provide.(ex.Video camera, computer access, talking to group members, assisting with an expert to contact etc..)Whatever you have accomplished by the due date I would like you to submit, even if it doesn’t turn out exactly as you thought it would.If you need an extension you must speak to me early regarding the reason for the request and then we will discuss it.
When is it due and how long does it have to be?
The Project Proposal sheet is due to me by Thursday, Febuary 11.
The presentation is to be submitted by Tuesday, April 14th or sooner.
As for the length of the project, the only direction I can give you is that it needs to be long enough to answer the question that you have set out.
