"Billy, can you tell us how many sixes there are in forty-four?.. OK, make it forty-two. How many sixes are there in forty-two? Billy, what is forty-two divided by six?.. How many times does six go into forty-two? Billy?? If I have forty-two chocolate brownies, and there are six people who want them, how many brownies does each person get?? Would it be seven? And if we started with forty-four, there would be two left over, right? Seven with a remainder of two.."
Most of us have been there. I know he can get it... If I just re-phrase it in a way he can understand...
An important item to consider when teaching math in any format is thinking time. Often, if we don't hear a response from a student, our instinct is to rephrase the question, or offer a quick hint or scaffold, or sometimes even answer the question for the students, with the hope they will be able to figure it out on their own the next time.
I have recently been in a fifth grade classroom and a Kindergarten classroom where I saw thinking time being offered to students in really effective ways.
The fifth graders, when given a question to ponder, were asked to put their pencils and papers away for a moment and discuss with a partner what strategies they might use to tackle the problem. When the discussion/ think-aloud time was up, students were asked to volunteer some of their strategies.
The Kindergarten students were told, simply, to stop and quietly think before raising their hand to offer a solution/ answer to a question. The teacher gave them about 10 seconds to think, and then when he signaled to them that the thinking time was over, the hands shot up in great numbers.
For me personally, I need thinking time in almost every situation. Not everyone does, but I do. Meetings are particularly difficult for me, because I am often two or three agenda items behind, stuck on something that was said when discussing an earlier topic. I then set myself up for embarrassment when I am called upon to voice my input on the current item.
"Umm... Could you repeat the question, please?"
For me, when other people are talking I have a hard time focusing on the appropriate topic. And for some of our students, it is even more challenging. Re-phrasing becomes more like another question added on top of the first one. Then the third re-phrasing is added, and now the student has three questions to consider. Indeed, some children have difficulty understanding that their teacher is trying to make it easier for them. Instead it feels like an interruption to an already challenging thought process.
Many students require time to process their thoughts. Pair-shares, quiet thinking time, and simply allowing some silence after questioning might make a significant difference in how confident your students' participation is in whole class or even small group discussions. This way, the worst case scenario is that there is an extended period of silence with no solution. And that is valuable for formative assessing. That extra little bit of time might yield a response from a student, and if not, you now know that student needs some help.
"Billy, it looks like you could use some time for this one. OK, let's all take 30 seconds to talk with a partner about how many sixes can fit into forty-four..."
Math lessons can be stressful for your students. Offering some quiet time to think gives them greater confidence when it comes time to present. It also gives them some ownership when sharing out, even if their answer is wrong. Thinking time helps them to own their mistakes, and to see those mistakes as an important step in the learning process. When there is not enough thinking time, students are more likely to panic and toss out a guess. And while a stab in the dark might get them a correct answer and a high-five from a neighbor, an incorrect guess has not meaning to them and is forgotten.
Thinking time helps reduce math anxiety and it helps kids see that making mistakes is an important part of problem solving.