To design instruction that allows a diverse class of students to move toward grade level standards, Marian Small (2009) suggests two core strategies. First, use open questions. Secondly, use parallel tasks, that are designed to meet the needs of students at different developmental levels.
Confident, engaged math students are contributors to classroom discourse because they know that their ideas matter, and they sustain effort by working through their mistakes. Their teachers use data to create specially designed instruction to meet their needs, at their instructional level, not on concepts that are already known or are too advanced. Further, teachers design frequent classroom discussions in which reasoning, not just correct answers, is valued. Students work in small or large groups to convince, question, and to be the audience for their peers as they discuss the ideas of mathematics and engage in problem solving. These teachers create good questions and then listen, provide input when needed, and allow students to do the reasoning. Learning mathematics is exciting and rewarding, and at times difficult, but allowing the time for thinking and drawing conclusions about well posed questions can empower students and enhance learning. Creating good questions can allow students to conceptualize the big ideas of mathematics at their own, varied developmental levels and move toward grade level standards in a meaningful way (NCTM, 2000).
To design instruction that allows a diverse class of students to move toward grade level standards, Marian Small (2009) suggests two core strategies. First, use open questions “framed in such a way that a variety of responses or approaches are possible” (p.6). Secondly, use parallel tasks, “sets of tasks, usually two or three, that are de- signed to meet the needs of students at different developmental levels, but that get at the same big idea and are close enough in context that they can be discussed simultaneously” (p.10). See this module on number sense for examples.
Suggestions for Creating Open Questions
1. Turning around a question (providing the answer and asking for a question, e.g. “You divide 2 numbers and the quotient is 40. List 5 possible pairs that you might have divided.”).
2. Asking for similarities or differences (between two concepts, numbers, graphs, etc.).
3. Replacing a number with a blank (allow student to fill in their choice of numbers).
4. Asking for a number sentence (provide certain numbers and words for students to include).
5. Changing the question by adapting a question from another source (Small, 2009, p.7).
Suggestions for Developing Parallel Tasks
1. Choose a “big idea” (e.g. you can see patterns in the way numbers are formed such as groups of 5’s or 10’s.)
2. Think about how students might differ developmentally in approaching the idea (easier patterns like even and odd numbers, v. more complex patterns such as multiples of 7) (Small,2009, p.11)
3. Develop similar tasks at differing levels (use the Tidewater Math Team’s Vertical Articulation by Topic resources for grades: K-3 and/or 3-6).
Developing Mathematical Thinking with Effective Questions
Teachers can use these questions at any point to support deeper discussions of mathematics. (broken link) http://www.pbs.org/teacherline/resources/questionsheet_vma.pdf
Teacher2Teacher resource regarding questioning (broken link) http://www.teachertoteacher.com/newsletter-archive/october-2009-newsletter.htm
National Council of Teachers of Mathematics. (2000). Principles of school mathematics, the teaching principle (Ch.2).Retrieved from (broken link) http://www.fayar.net/east/teacher.web/math/Standards/document/chapter2/teach.htm
Small, M. (2010). Gap closing: Number sense grade 6 facilitators guide. Edugains: Ontario, CA. Retrieved from http://www.edugains.ca/resources/LearningMaterials/GapClosing/Grade6/GCU1_FG_RepresentingFractions.pdf
Small, M. (2009),.Good questions, great ways to differentiate mathematics instruction. Reston, VA: NCTM.