I’ve been lucky enough to have attended a couple of workshops run by Dr Cathy Marks Krpan. She is a dynamic presenter and passionate about the power of oral and written communication to develop student thinking, understanding and problem solving.

In the book the author does discuss the theory and research behind the strategies but it is essentially an excellent collection of practical suggestions, teaching strategies, assessment tips and worked examples (strategies in action).

Each of the 29 teaching strategies is clearly explained with printable materials, sample implementations, modifications and extensions. Strategies in action show annotated examples of students’ work from kindergarten through Grade 8.

The book has an excellent accompanying website with links to professional resources and downloadable tools and line masters.

My favourite take-away from Cathy’s PD sessions was mathematical proofs whereby the students explore a mathematical statement and have to prove that it is either true or false. I used the example below as a summative assessment to our unit. I was impressed by the variety of ways this student was able to demonstrate their understanding using manipulatives, fraction circles, equivalent fractions and decimal conversions.

**Other favorites from the book:**

**It Is and It Isn’t**– students work with a partner to discuss a mathematical concept by describing what it is and it isn’t

student 1: It is a triangle because it has 3 sides

student 2: It is not a square because it does not have 4 right-angles

student 3: It is a polygon because it is a 2D shape with straight sides

student 3: It is not a circle because it does not have a curved side

student 4: It is a regular shape because all its side and angles are equal

**Frayer Model and VVWA charts**– graphic organizers to help students develop (or teachers to assess) vocabulary and conceptual understanding (download from here)**Gallery Walks**– good tips for how to organize a gallery walk and teach students howto give descriptive feedback**Show Me the Math!**– develops visual literacy skills by encouraging students to take the time to see the maths in their everyday environment. Choose a photograph or object that can be connected to several mathematical concepts (example shown is an area in our playground) and ask the students to describe any maths they see and explain their thinking.

- the face of the dog is symmetrical because it is the same on both sides
- the back of the bench has parallel lines because they are the same height
- I see a right-angle made by the leg of the bench
- the legs of the bench are cuboids because they have 6 rectangular faces