I have had several emails/messages this summer from colleagues wondering and thinking about the teaching and learning of mathematics through inquiry. Our redesigned curriculum here in BC highlights big ideas at each grade level, in each curricular area. One pedagogical approach to develop students’ understanding (the U in the KDU framework) of the concepts embedded in a mathematical big idea is to provide questions to inspire student inquiry. These questions may be provided as a provocation to individual students, to small groups or to the whole class. Students may work on different questions over time, all connected to a big idea. There are many different ways these open-ended questions may be used in the classroom and are an inclusive practice as they provide entry points for all students to engage in mathematics. These questions invite students to engage with materials and mathematical ideas…some examples:
How many different ways can you decompose 10?
What is the relationship between multiplication and division?
What makes a fraction a fraction?
Through students’ investigations, mini-lessons, scaffolding and prompting from the teacher, students are guided to uncover mathematical content and knowledge (the K in KDU) through experiences that also focus on developing curricular competencies or the doing of mathematics (the D in KDU) such as reasoning, problem-solving, making connections and communicating thinking.
A group of us worked together to create questions that correspond to the new math curricular content and competencies. These questions were inspired by the elaborations for the science curriculum, that had been well received by teachers in BC. The questions are meant as starting points for mathematical inquiry and investigations and may be used to frame a series of varied but related learning experiences. They are written to potentially inspire cross-curicular inquiry as well as integrating the First Peoples Principles of Learning. These elaborations are currently being hosted on the BCAMT website until they are uploaded to the Ministry’s curriculum website. The K-9 document can be found HERE. The following is an example from Kindergarten:
It is essential that students’ background, interest, experiences and understanding inform the questions that are provided to them. Many teachers like to have questions to begin with, that they can then adjust and adapt for their students. There are many sources for these types of questions, as a starting point.
Resources I recommend:
by Pater Sullivan and Pat Lilburn (elementary version)
Good Questions for Math Teaching: Why Ask Them and What to Ask
by Lainie Schuster and Nancy Anderson (middle school version)
These four books are all available in many catalogues and online sources.
A new series of books from Canadian Dr. Marian Small – Open Questions for Rich Math Lessons, They can be ordered through Rubicon Publishing HERE.
For those of you who have been following along with our Reggio-Inspired Mathematics project, there is a blog post with various question frames that we use as we co-construct provocations for our students. It can be found HERE. We have developed provocation postcards for K-2 and are working on postcards for 3-5 and 6-9. They have a photograph and one question on the front and a collection of related questions on the back – all connected to one mathematical big idea.
The questions we pose as teachers are important – they need to be responsive and intentional. But, I also think there needs to be space for students to pose their own questions. Something that I have noticed as I work with teachers and students who have been using these types of questions over the last few years is that the students begin to ask these questions of themselves and each other. It is very empowering for the students to be the ones asking the questions that frame the learning experiences in the classroom. I believe its essential to find opportunities and openings for the students’ own questions in classrooms. But that is another blog post…or maybe a dissertation