You can read about how I use the following math talk cards here - http://www.peachy-teaching.com/2013/09/number-talks-and-freebie.html
These cards are a great way to guide and support students as they begin engaging in math talk activities (also called number talk). Each card has a sentence stem to get kids started talking.
Simply print and cut the cards. Punch a hole and put the sets together with a ring clip.
101questions, with common math questions seen in the real world. Resource for teachers of math to bring real math into the conversation and begin (or end) a class session.
Cowbird, a site with photos and stories. Great place to have students think and describe in their writing
Using Questioning To Stimulate Mathematical Thinking Grouped mathematical questioning into four main categories (Badham, 1994). These questions can be used be the teacher to guide the children through investigations while stimulating their mathematical thinking and gathering information about their knowledge and strategies.
Consider this statement. Which is correct?
A boat carrying a large boulder is floating on a lake. The boulder is thrown overboard and sinks. The water in the lake (with respect to the shore)
3. remains the same.
For many students, math questions always come out of a text book or a worksheet. The questions are usually along the lines of "here’s a word problem - take the figures, plug them into the given formula, do some calculation and move on to the next one."
But it’s great to trigger the students into asking their own questions. This is more likely if the question is conceptual and interesting, rather than calculation-based. The above example (from Asking good questions in the mathematics classroom) is more likely to illicit a lot of genuine discussion than the normal text book question.
Here’s another one from that paper:
Imagine that you are sky-diving. The graph of your speed as a function of time, from the time you jumped out of the plane to the time you achieve terminal velocity is most likely
a) Increasing concave down.
b) Decreasing concave down.
c) A straight line with positive slope.
d) Increasing concave up.
There’s quite a bit going on here. A lot of conceptual understanding can result - and no calculation is needed!
Once students get used to this level of conceptual question, it is more likely they will ask deeper, more meaningful questions about what is going on.
Students gain a lot of insight into math when they have to create their own questions.
One simple idea to get the students into this is to get them to write questions for the mid-semester test (say). You could assign sub-topics to small groups of students and get them to propose 2 or 3 questions. It’s surprising how well this demonstrates whether students really do understand what they’ve been doing. It also lets them see math from a broader perspective.
Then, get them to share their questions around the room and solve them. Some of them may be impossible to solve - it can be transformational when they discuss what’s wrong with the question and then feed back their conclusions to the question posers.
They could do this using Google Docs (or a wiki) so there is a record of the thinking and problem solving process.
This will seem a crazy idea to start with, since it’s very unusual in math class. However, it can be very beneficial for learning. (Reflection is a key element in efficient learning.)
Students don’t see the value of writing about their math thought processes at first, but once they see how it can help them clarify their doubts, they become more enthusiastic about it.
This short article includes some ideas on the kind of questions you can use to prompt reflection in math:
Here are some more good ideas: