Presentation by George Gadanidis, 2 September 2021
What’s new in Grade 9?
- some new big ideas of mathematics (infinity & limit in the context of natural density)
- coding as a tool
- students research & tell a mathematics story
An example from Number
- d(even numbers) = 0.5
- what is the probability that a random natural number is odd?
- d(multiples of 5) = 0.2
- what is the probability that a random natural number is a multiple of 5?
- d(multiples 0f 10) = 0.1
- what is the probability that a random natural number is a multiple of 10?
NATURAL DENSITY OF SQUARE NUMBERS
- d(square numbers) = 0
- what is the probability that a random natural number is a square number?
How do we make sense of d(square numbers) = 0 ?
Here is one way …
2 PAGES FROM MATHEMATICS GRADE 9
Here is the completed table.
The Scratch code shown above is available at https://scratch.mit.edu/projects/565845359/editor
Infinity & limit in grade 9?
The short answer is: Mathematics is big but kids’ minds are bigger!
If you visit St. Matthew the Evangelist Catholic School in Whitby, Ontario, you will see this large painting in the front foyer, depicting the work of grade 3 students (over 10 years ago), as they learned to hold infinity in their hands.
See also a workshop on infinity & limit at https://learnx.ca/infinity.
How to approach coding
Start with code that works
- Have students execute the code to see its output
- Ask them to alter the code to model the different intervals in the table
- Ask: how does the code do what the table does?
- Ask them to share what they understand and what they have questions about
- Have students try to answer one another’s questions
- Don’t be in a hurry to explain
YOU DON’T HAVE TO BE THE EXPERT
- Make “understanding” their problem
- Print and post the code on a whiteboard
- Draw arrows to the parts that students are unsure about
- Students can use sticky notes to write/post description of what the code sections do
- The more you explain the less they will think about it
GET READY TO BE SURPRISED
- I’ve spend many, many days in grades 1-10 classrooms co-teaching math + coding
- A common event is teachers telling me to look at a student whose engagement and understanding surprises them
CODING OFFERS ADVANTAGES
- Models mathematics concepts & relationships dynamically
- Makes abstract ideas feel tangible
- Offers agency
- Offers a low floor and a high ceiling
DON’T TEACH CODING, TEACH MATH
- The fad around us is to teach all kids how to code
- Our job is to teach all kids about the structure, beauty and wonder of mathematics
- Coding is a great tool, in some mathematics contexts
The Mathematics Grade 9 resource
- BOOK A – Teaching support
- Curriculum expectations
- Trajectories, surprises & insights
- Success criteria
- Teaching suggestions
- BOOK B – Number
- for teachers & students
- BOOK C – Algebra
- for teachers & students
… more coming soon