Teaching mathematics for a growth mindset#
See als: teaching-mathematics, design-for-mathematical-mindset, growth-mindset
Summary of chapter (of the same name) from Boaler (2015)
offers a shorter summary of many of the ideas from the book, pulled together to give a move concise guide to setting up a growth mindset mathematics class
Class norms#
Tell them beliefs - I believe in every one of them, that there is no such thing as a math brain or a math gene, and that I expect all of them to achieve at the highest levels. - I love mistakes. Every time they make a mistake their brain grows. - Failure and struggle do not mean that they cannot do math— these are the most important parts of math and learning. - I don’t value students’ working quickly; I value their working in depth, creating interesting pathways and representations. - I love student questions and will put these onto posters that I hang on the walls for the whole class to think about.
Establish norms poster
- Everyone can learn math to the highest levels
- Mistakes are valuable
- Questions are really important
- Math is about creativity and making sense
- Math is about connections and communicating
- Depth is much more important than speed
- Math class is about learning not performing
Example - Participation quiz#
Gives a detailed example of using participation quiz from "complex instruction" work
Opening mathematics#
Teaching mathematics as an open, growth, learning subject#
Move away from narrow and procedural questions that require calculation. Give more open questions that provide an opportunity to grow.
Encourage students to be mathematicians#
Proposing ideas aka making conjectures about mathematics.
Teach mathematics as a subject of patterns and connections#
"Mathematics is all about the study of patterns" - encourage students to be pattern seekers. Mathematical methods are the result of patterns
"Curriculum standards often work against connection making, as they present mathematics as a list of disconnected topics. But teachers can and should restore the connections by always talking about and valuing them and asking students to think about and discuss connections." (p. 184)
Youcubed - tour of mathematical connections
Teach creative and visual mathematics#
Having students draw the mathematical concepts they're working on.
"Representing mathematical ideas in different ways is an important mathematical practice, used by mathematicians and high-level problem solvers" (p. 188)
Encourage intuition and freedom of thought#
mathematicians heavily rely on intuition, mathematics education not so much.
Ask students to develop their own method (intuitively) before presenting formula
- How to measure the height of an object to high to measure?
- What's the volume of a lemon?
Touching on the direct instructions/inquiry learning debate but emphasising the benefits of inquiry learning.
Value depth over speed#
Touches on observations of mathematics lessons in China - top of PISA results - that show an inquiry emphasis in the pedagogy. Raising questions about representativeness.
Connect mathematics to the world using mathematical modeling#
Cites interviews of young adults complaining about how mathematics is prevalent in what they observe, but they never knew (from their math education)
pseudo contexts
Model with mathematics#
Lots of discussion/examples
- Encourage students to pose questions, reason, justify, and be skeptical
"The first thing a mathematician has to do is post an interesting question" (p. 204)
Given a context/set up
- We wonder (a question)
- We want to investigate
Teach with cool technology and mainipulatives#
References#
Boaler, J., & Dweck, C. (2015). Mathematical Mindsets: Unleashing Students' Potential Through Creative Math, Inspiring Messages and Innovative Teaching. John Wiley & Sons, Incorporated. http://ebookcentral.proquest.com/lib/griffith/detail.action?docID=4444210