Math Talk
Coach's Corner by Engy Boutros
The Big Picture
- A good math student can see the math. Seeing the math means visualizing the process, making the connections to previously learned concepts and extending the concepts to help solve unfamiliar problems.
- Our everyday life provides the context.
- We use math to help us solve problems.
- Graphical models help us analyze and look for patterns.
- Algebraic models provide a method for making predictions and looking for solutions.
- Words are translated to math in order to make analysis concise and doable.
- It is important to teach students the whys and the hows. (Procedural vs. Conceptual understanding...we should continually be asking where is the thinking in our teaching?)
Mathematical Processes
Grade 9: The Line
Relationships can increase at a constant rate or decrease at a constant rate.
y = mx + b
Possible Guiding Question:
How can math help me make some important financial decisions?Grade 10: The Parabola
Things don't always increase or decrease at a constant rate. Numbers can increase and then decrease again or start off decreasing and then increase.
y = ax^2 + bx + c
Guiding questions:
Where will the ball land? How far will it be?
What is the largest area?
What is the safest height and width for the bridge?
Parabolic Bridges
The Ball Throw
Maximizing the area of a rectangle
Grade 11 and beyond : Functions
Guiding question:
How can we use functions to model real life data? (e.g. the motion of a swing, the rise and fall of tides, the rapid decay of radioactive substances, the growth rate of bacteria, population growth, the accumulation of interest, the depreciation of valued goods etc...)
Halls Harbour Tide, Time Lapse
Periodic Functions
Rise and fall and return back to starting point again.
http://blog.mrmeyer.com/2014/confab-design-a-new-function-carnival-ride/
Exponential Growth
The rapid rise of Ebola cases can be modeled with an exponential function.
Exponential Decay
Assessments
In addition to the traditional test and quizzes why not use interviews, art projects, performance tasks, data collection and analysis?
High importance on feedback and self assessment and less importance on grades.
When students ask if it counts answer :
"It counts for learning"!
Math Anxiety
Millionaire Math
Mindset and Anxiety
What happened when she saw the question?
What made the task difficult?
Was she able to do the question?
How does this relate to our students?
What our students are saying...
EQAO survey
What teachers can do to promote a growth mindset and decrease math anxiety...
What a positive math class looks like...
Dan Meyer on Real-World Math
Why teaching procedures and algorithms is not enough?
Why is Math Different Now
Students at work
Sample Assessments
Super Stairs
How many processes are involved in this task?
Who says there is no room for manipulatives?
Integers, Expanding, Factoring and Completing the Squares
The abstract world of algebra can be made concrete through the use of algebra tiles.
Many great tasks on the OAME TIPS4RM site.