Differentiation in math is a relatively new idea. While it has become an integral part of any literacy program, it is scarcer in math. DI requires more planning and thinking through the logistics. Teachers may sometimes be reluctant to use it, because the majority of us experienced math as a subject in which everyone was on the same page. Deviating from the textbook was not encouraged. The class moved forward in lockstep. There was little room for varying the content, process or product.
Many of the questions we traditionally ask students call for a single number, figure, or mathematical object. These kinds of questions are closed because the expected answers are predetermined and specific. Conrad Wolfram estimates that they make up around 80% of math instruction! Students are sent the message that math is about simply finding the right answer. It is black or white. A static subject with no creativity that only relies on a series of endless computations. Motivation to learn math is lost. No wonder students tune out beyond a certain point.
Open questions, an approach popularized by Canadian math researcher Marian Small, offer an alternative. Creating a question that allows for multiple entry points gives all students the opportunity to find something meaningful and appropriate to contribute. They offer a variety of responses based on the students’ level of content knowledge and understanding. This gives students the confidence that is sometimes lacking in math class. Levels of anxiety are reduced as open questions close the various ZPD gaps among the students.
Math is seen as multi-faceted. The subject comes to life.
The best open questions have a low floor and high ceiling. This effectively levels the playing field and gives more students a chance to engage in math. Open questions should focus on big ideas and curricular goals. They need just the right amount of ambiguity, ensuring that the question is broad enough to meet the needs of all students. Strategies for creating open questions:
- turning around a question (think Jeopardy)
- asking for similarities and differences
- replacing a number with a blank
- creating a sentence using certain concepts/definitions/numbers
- using ‘soft’ vague words for flexibility
The first thing a mathematician has to do is pose an interesting question. These are virtually absent in most math classes today. Open questions are a way to change this.