I have been researching the use of ‘good’ questions in math via the book Open-Ended Maths Activities by Peter Sullivan and Pat Liburn. This book challenges teachers to think more deeply about math questioning and about providing students with opportunities to show the depth of their thinking. It places math understanding on a continuum and allows you to really see the thinking process that children go through when solving problems. The problems differ from ‘regular’ math questions in that the focus in not necessarily on THE right answer, but more on the process of problem solving, predicting, refining thinking, justifying decisions and creating own like problems.
The three main features of a ‘good’ question:
- They require more than remembering a fact or reproducing a skill
- Students can learn by answering the questions, and the teacher learns about each student from the attempt
- There may be several acceptable answers
In partners, we started with this question:
We will take a look at the different strategies people used and then move on to a more challenging question. As children work, I am looking at the following behaviors (not all at once, but throughout the process):
- works cooperatively
- works independently
- makes a plan
- keeps trying
- when stuck, tries something different
- discusses work with others
- uses materials when useful
- draws diagrams when necessary
- concentrates on the task
- asks questions
- organizes information systematically
- explains and displays ideas clearly
- looks for all possibilities
- able to generalize
- accepts assistance from others
- is confident
- uses a range of mathematical strategies
After the kids finished their work, I scanned it and shared my thinking with them as I went through their responses. This was probably the most valuable part of the lesson – and the part where we begin to put into practice the idea of growth mindset. By actively illustrating what I am thinking and where I see the next steps for all groups of children, it promotes the idea of deeper learner for all. What I like about this approach is that there is feedback that is applicable for all students and everyone can see something that they can look to improve on during the next question. We did this on our smart board with the whole class. Here are samples of some of the feedback I gave my students:
Our next step was to stay in our partnerships (mixed ability) and tackle a few more questions of increasing difficulty. Each time, I scanned their papers and we discussed and gave feedback as a group. Toward the end, the students were very adept at indicating the strengths of the teams and offering suggestions for growth.
We have now moved on to applying our problem solving strategies to a weekly math challenge. A math challenge is a problem that is designed to last more than one lesson before a solution is found. It is a chance to show what you know about math, to make predictions, to create your own problems, and to share your reflections on yourself as a mathematician.
Each week, we will have a new math challenge. It can be solved independently or in a small group. It can be done at home or at school. It has a due date (usually will be on Friday), and it is designed to help students apply what we are working on or skills that have been focused on in class already.
Each math challenge comes with the same list of ten criteria. Each of these criteria is equally important. Students are challenged to respond to each of the criteria to the best of your ability. These criteria will be the same each week.
Here is our first question:
You might notice the quote at the bottom of the question slip. After reading the work of Carol Dweck on establishing a growth mindset, I then saw that the Khan Academy have also utilized this research and have found a way to improve student performance via one simple trick: adding a growth mindset inspired quote to their math pages. This is just one way of reminding students or drawing their attention to the fact their brains are capable of growth and new learning.
We just started this today and worked on it for about fifteen minutes. The kids were super excited and it was great to see them tackle this problem with such a high degree of independence.
After setting this up, I was reminded of a post I read recently about additive grading. I am now rethinking how I am going to grade this to some degree. But that’s for another post…