A few days ago, I was in a professional development meeting with paraeducators at C.P. Smith Elementary School. We were discussing how best to help students in math. We had a great conversation about it and talked about the idea of asking instead of telling. Our focus was #1 and #3 of the eight Common Core Math Practice Standards. I’d printed some questions that I have seen on several different websites, so I am not sure of the original author. Here they are:
Make sense of problems and persevere in solving them
- How would you describe the problem in your own words?
- How would you describe what you are trying to find?
- What do you notice about...?
- What information is given in the problem?
- Describe the relationship between the quantities.
- Describe what you have already tried. What might you change?
- Talk me through the steps you’ve used to this point.
- What steps in the process are you most confident about?
- What are some other strategies you might try?
- What are some other problems that are similar to this one?
- How might you use one of your previous problems to help you begin?
- How else might you organize...represent... show...?
Construct viable arguments and critique the reasoning of others.
- What mathematical evidence would support your solution?
- How can we be sure that...? / How could you prove that...?
- Will it still work if...?
- What were you considering when...?
- How did you decide to try that strategy?
- How did you test whether your approach worked?
- How did you decide what the problem was asking you to find? (What was unknown?)
- Did you try a method that did not work? Why didn’t it work? Would it ever work? Why or why not?
- What is the same and what is different about...?
- How could you demonstrate a counter-example?
After the paraeducator meeting, I came across an Edutopia article entitled, “Takeaways from Math Methods: How will you teach effectively?” It is about pre-service teachers who have taken a math course. This jumped out at me.
Helping Students Doesn't Mean Showing Them How
Before admitting [preservice teachers], we interview each one and ask, "Why do you want to be a teacher?" The most common response is, "I want to help students," a sentiment that PSTs describe later as "giving good explanations" or "making it simpler" -- notions of helping which are underdeveloped.
A synthesis of research in mathematics education by James Hiebert and Douglas Grouws identified two teacher actions that impact conceptual understanding. One is to engage students in productive struggle. Merely telling students how or making things simpler does not actually help them understand as much as providing challenging tasks and time to "dig in" to a problem.
To help them redefine how to help students learn, I encourage [teachers] to embrace their sense of accomplishment when they solve a challenging task, recognize the pride they feel when they share a unique way to solve a problem, and reflect on what such feelings might mean for a student in their own classroom.
The way this piece is written states an important idea in a concise, clear way. I hope to keep pushing myself and others to ask, watch, and listen instead of show and tell.