learning through problem solving with john scammell
DESCRIPTION
Learning Through Problem Solving with John Scammell. Developed by ERLC/ARPDC as a result of a grant from Alberta Education to support implementation. John can be contacted at. [email protected] Twitter: @ thescamdog Blog: www.thescamdog.wordpress.com. Objectives. - PowerPoint PPT PresentationTRANSCRIPT
Learning Through Problem Solvingwith John Scammell
Developed by ERLC/ARPDC as a result of a grant from Alberta Education to support
implementation
This session is aimed at High School Math teachers and is intended to help support the implementation of the revised program of studies.
Participants will see examples of how students can learn THROUGH problem solving.
Objectives
ERLC – Learning Through Problem Solving
In the polling response section, please enter◦ A if you are a High School Teacher◦ B if you are a Junior High School Teacher◦ C if you are an Elementary School Teacher◦ D if you are a consultant or administrator◦ E if you are some combination of the above
Who is Here?
ERLC – Learning Through Problem Solving
In the polling response section, please enter◦ A if you are from Edmonton◦ B if you are from the greater Edmonton area◦ C if you are from elsewhere in Alberta◦ D if you are outside of Alberta
Who is Here?
ERLC – Learning Through Problem Solving
There are seven mathematical processes in the front matter of the revised program of studies. These processes are to permeate teaching and learning.
◦ Communication (C)◦ Connections (CN)◦ Mental Math and Estimation (ME)◦ Problem Solving (PS)◦ Reasoning (R)◦ Technology (T)◦ Visualization (V)
Alberta’s Revised Program of Studies
ERLC – Learning Through Problem Solving
“The mathematical processes are the content, and the outcomes are the context.”
Dr. Peter Liljedahl, Simon Fraser University – Secondary Math Education
Alberta’s Revised Program of Studies
ERLC – Learning Through Problem Solving
The description of the Problem Solving process contains the phrase:
“Learning through problem solving should be the focus of mathematics at all grade levels.”
Alberta’s Revised Program of Studies
ERLC – Learning Through Problem Solving
We learned FOR problem solving.
In the old days…
ERLC – Learning Through Problem Solving
In the old days…
ERLC – Learning Through Problem Solving
The top of Ken’s new desk is m wide and m long. Find the area of the top of his desk.
3 1 5
We learned ABOUT problem solving.
Then we thought we improved it…
ERLC – Learning Through Problem Solving
Then we thought we improved it…
ERLC – Learning Through Problem Solving
1. Understand the Problem
2. Develop and 3. Carry Out a Plan
4. Look Back
ERLC – Learning Through Problem Solving
Learning through problem solving should be the focus of mathematics at all grade levels.
- Alberta Program of Studies
ERLC – Learning Through Problem Solving
An example of learningTHROUGH
problem solving.
http://www.amaranthpublishing.com/MozartDiceGame.htm
ERLC – Learning Through Problem Solving
Mozart's Dice Game
Please roll your dice and enter the results.
Mozart's Dice Game
http://sunsite.univie.ac.at/Mozart/dice/collaborate.cgi?tables=yes
ERLC – Learning Through Problem Solving
Mozart's Dice GameIf this is an activity used in class, the next thing I would tell the students is that I am incredibly confident that no one else has ever heard the minuet they just played. What questions might they have? Can we distill it down to one single question?
ERLC – Learning Through Problem Solving
Possible questions:
Has the minuet we just composed ever been heard before?
How many minuets could be created using the parameters of the problem?
How long would it take you to listen to them all, assuming that each takes about 30 seconds?
Mozart's Dice Game
ERLC – Learning Through Problem Solving
Mozart's Dice Game
Debrief. Discuss.
What mathematical concept is addressed?
Could students arrive at this concept on their own?
Where will they struggle?
How will you scaffold for those who struggle?
ERLC – Learning Through Problem Solving
What makes for a good problem for learning through problem solving experience?
Components of a good problem:
The problem is given at the beginning of the learning rather than at the end.
The problem is non-routine. The students can not solve it immediately. But,
Every student has an entry. The problem is engaging and compelling so students will
persevere. The problem invites multiple methods of solution. The problem fosters discussion and debate. The problem is at an appropriate level for the audience. The best ones allow the students to come up with their own
problem to solve.
A compilation from a variety of sources – Marilyn Burns, Marian Small, John Van de Walle, Dan Meyer, and me.
One of the great problem solvers of our time…
“The definition of a good mathematical problem is the mathematics it generates rather than the problem itself.”
“It's fine to work on any problem, so long as it generates interesting mathematics along the way - even if you don't solve it at the end of the day.”
“I loved doing problems in school, I'd take them home and make up new ones of my own.”
Andrew Wiles
ERLC – Learning Through Problem Solving
Another Example of Learning Through Problem Solving
Laura has trained her pet rabbit, Jack, to hop up a flight of 7 steps. Jack can hop up one step at a time or two steps at a time. How many different ways can Jack hop up the flight of seven steps?
ERLC – Learning Through Problem Solving
Rabbit Problem Debrief
Debrief. Discuss.
What mathematical concept is addressed?
Could students arrive at this concept on their own?
Where will they struggle?
How will you scaffold for those who struggle?
Discuss:What does your classroom look like when kids are working on problems?
Learning Through Problem Solving What does your classroom look like while
students are working on problems? How do you debrief the problems with
students? Do you tell them the right answer? Where do you find these problems?
ERLC – Learning Through Problem Solving
When a problem is not particularly
compelling, how do we engage students?
Measurement - Math 10C &10-3
An example of learningTHROUGH
problem solving.
From worst to better…
From Dan Meyer’s Blog (dy/dan)
http://blog.mrmeyer.com/?p=5983
ERLC – Learning Through Problem Solving
Measurement
Worst
•The problem claims to represent the real-world but its illustration is only clip-art or a line drawing.
•The problem specifies the exact method of its own solution, usually in a series of substeps labeled "a, b, c, d.“
•The problem only gives information that the student will use in the solution.
ERLC – Learning Through Problem Solving
Measurement
Bad
The same as worst except:The real-world problem presents itself as it exists in the real world.
ERLC – Learning Through Problem Solving
Measurement
GoodThe same as bad except:
The problem reveals no information about itself — no measurements, especially — forcing the student to decide for herself what information is relevant to the solution.
The problem doesn't hint at its own solution method with sub-steps. The student can develop that solution socially, in conversation with her teacher or her classmates.
ERLC – Learning Through Problem Solving
MeasurementAn example of learning
THROUGH problem solving.
… to Best
http://vimeo.com/9552977
ERLC – Learning Through Problem Solving
Measurement
BestThe same as good except:
The problem hangs itself on a single, concise, intuitive question, one that any student can answer, regardless of mathematical ability. The teacher solicits guesses and records them publicly, investing the students in the outcome of the exercise, and refers back to them later, perhaps introducing the concept of percent error.
The solution to the problem isn't read from an answer key. Instead, it's observed by the class together in a second multimedia artifact. The class compares the answer derived from their theoretical model to this practical answer. This is scary. The class will almost certainly be wrong but the conversation about sources of error should be embraced, not feared.
ERLC – Learning Through Problem Solving
ERLC – Learning Through Problem Solving
Homework: If you haven’t seen Dan Meyer’s TED Talk, you need to go home tonight and
watch it.
http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
ERLC – Learning Through Problem Solving
What I tried based on Dan’s ideas
Math 10 Applied – Angle of Elevation and Depression
1. Students measured heights of their eyes.2. Students found one object in the classroom
that was the same height as their eyes.3. Students moved around the room and listed
objects they would have to look up to see (elevation) and down to see (depression).
ERLC – Learning Through Problem Solving
What I tried based on Dan’s ideas
Math 10 Applied – Angle of Elevation and Depression
4. I took the class to the atrium and asked them, in teams of three, to estimate the height of the second floor railing above the main floor.
5. We returned to the classroom and recorded each team’s guess in a chart on the SMART ™ Board.
6. We made clinometers, and each team had a clinometer and a tape measure.
ERLC – Learning Through Problem Solving
What I tried based on Dan’s ideas
Math 10 Applied – Angle of Elevation and Depression
7. They returned to the atrium to calculate the actual height of the atrium.
8. Each team recorded their calculated height next to their estimate.
9. We revealed the actual height, and celebrated the best estimate and the best calculation.
A quick question that promotes thought and exploration is valuable.
Learning through problem solving doesn’t require lengthy projects.
ERLC – Learning Through Problem Solving
What Sam Shah www.samjshah.com used
A Math 10C Teacher Shared
Let’s Try One More:
Looking at this illustration, what questions do you want to answer?
From Andrew Shores at http://andysunknownquantity.blogspot.com/
Extensions
Can the grasshopper start on any particular number (not counting shaded boxes) and be safe by taking hops of 4?What if it took hops of 5? 6? 7? What if the spider webs were on perfect cubes? What if they were on triangular numbers? Fibonacci numbers? etc.
ERLC – Learning Through Problem Solving
Thank you for participating
John Scammell can be reached at:
Twitter@thescamdog
Blogwww.thescamdog.wordpress.com