Our math classrooms are more and more diverse each year. Learners come to us with a range of different experiences and levels of understanding of the mathematics that’s important to know. Meeting the needs can prove challenging. Dr. Marian Small’s book called Good Questions: Great Ways to Differentiate Mathematics Instruction is an excellent resource for learning how to craft questions to make the math accessible to all – challenging for those who need it, and simplified for others. Check it out for more rich and open tasks to engage children in thinking mathematically across the grades!
This is an incredibly useful teacher resource book. In it, Dr. Small poses open-ended questions across the strands as well as what she terms “parallel tasks”, which present the same math concept at 2 different levels of complexity. It’s a very clever way to include everyone in the mathematical discussion, and can really help when we’re planning for instruction in a combined grade setting. Oh – and did I mention that Marian Small is Canadian?? 🙂 Her work is in line with the WNCP math curriculum and so makes a great match for anyone teaching math here in Canada.
This selection of questions from Dr. Marian Small’s book are ideal for combined grades settings, since they address big math ideas that are common to side-by-side curricula. Invite your students to represent their thinking with models, pictures and words, and to share what they know with a peer, a small group and/or the class. These questions lend themselves to rich classroom discussions, and can give you as a teacher important assessment data to inform your planning.
PS – Marian Small has also authored a companion book for secondary math that’s well worth checking out: MORE Good Questions: Great Ways to Differentiate Secondary Mathematics Instruction.
Last week I gave a session for teachers in Coquitlam looking to teach – and assess – problem-solving. We talked about what made a good problem, both in terms of content and wording, then worked through some samples across the grades. I have posted a selection of problems for you here, which I invite you to download and use with your students.
Remember that it’s important to collect students’ thinking in a variety of forms – numbers, pictures and words, to have them engage with models or manipulatives, and wherever possible to have students communicate their understandings about a concept by translating them to a problem of their own. The latter is no small task! :o) John Van de Walle’s diagram outlines the importance of not only including these representations but also connecting and bridging between them. Students learn deeply when they transform their learning from numbers to models, from words to pictures, from problems to numbers and back again…