Once you have identified the behaviours that act as barriers and explored the motivation behind them, you can employ effective strategies to help students participate in and contribute to the mathematical talk in the group.
The following strategies are derived from research, teacher discussions at ALiM expo days, and the reflections of teachers in charge of ALiM programmes. While effective practices in facilitating classroom dialogue are useful for all students, the following have been successful specifically with the target groups.
1. Remove the spotlight from individuals
Consider the experience of the underachieving student who feels the intense glare of the spotlight when asked for a contribution, such as an answer to a problem or an idea to share. Try to avoid having anyone respond individually. Stress the collective pronouns of “we” and “us” and provide students with the support of working as a pair or triad and contributing as a team. Honest praise, encouragement, and critique are then given to the group, not to the individual. This practice may support silent students to be more vocal, first within their pair and then with their pair in the wider group. This practice also reduces the need for piggybacking, especially when there are only two discussing something or getting ready to share.
2. Shift attention from answering to evaluating
Instead of posing problems that require calculation before engaging with concepts, turn things around and eliminate the need to come up with an answer. Evaluate a fictional student’s answer to build confidence and break down the “teacher questions – student answers” dialogue model.
Here is someone’s work on a sharing problem. I wonder if we can follow their thinking. Tell me what you see.
How do we think they arrived at this answer?
If we could ask them to add one thing that would make this clearer for us, what would we want?
OK, so we think a diagram here would help us know where these numbers came from. I wonder what sort of diagram we could suggest?
3. Model thinking by thinking aloud
How can we support students who don’t know what to do when told to Have a think before you answer?
An effective method is to model what thinking sounds like by speaking your own thoughts out loud and being very specific about what steps you are going through to form a response. Students’ expression of their thinking gets better with practice provided they know what they are expected to be doing.
The random guessing and distraction tactics used by some students may reflect a high level of confusion. They may not understand how other people are actually getting answers to maths questions or what other people “see” in their heads. By opening up the process of engaging with a problem, working through different ideas, and identifying points of confusion, you can provide critical insight for students.
OK, I’m going to take a turn now and share my thinking as I solve 32 + 41. I look at this equation, and I know I’m going to be using tens and ones. So I imagine 32 on the hundreds board. I know I have to add on 40 and I have to add on 1. That is 4 tens or like going down 4 whole rows. So I think: 10 more is the next row – I’d land on 42, then 52, then 62, and the fourth row is 72. And then add on 1, so that’s 73. I think I’ve got an answer, but I want to write down the number and check my thinking. (If I keep the numbers all in my head at the same time, sometimes I get mixed up.) So I write down 73 and look at all the numbers together and see if it makes sense. It looks right because I know it can’t be more than 100 because it’s only a 30s number and a 40s number.
4. Revoice instead of questioning in order to guide discussion
Some students, especially those who have had negative experiences, can view questioning as confrontational. They may perceive a question as a personal challenge instead of a scaffold or support for their learning. Revoicing is an effective technique for guiding students to communicate in mathematically meaningful ways. It involves repeating student talk, rephrasing it, or expanding on it, using their own words as the springboard for the discussion. By revoicing, you can highlight ideas that originate with students, further develop implicit meanings within those ideas, and add new ideas to the discussion.
Sam and David were given 11 strawberries. How many strawberries does each get if they share them?
Student: We think when you share these, you each get half. So, 5. But you still have 1 left, so then you’ve got to break that 1 too, but it’s only a piece. So we think maybe you each get 5 and a quarter. It’s not like other double and halves.
Teacher: What I hear is that you think this is a different sort of problem – that you noticed it’s not even when you share them out. I can see how you have 5 here and 5 here and then this 1 left over. You’ve decided it needs to be broken?
Student: Yes, because you can’t just leave it over because everything needs to be shared. So we’re going to break it. In half – oh, like 2 pieces. So, you get 5 and a half!
Teacher: So you’ve changed from half of 11 is 5 and one quarter to 5 and one half …
Student: Yes, because half is when you break in two, and quarter is breaking in … um, four?
By employing extra support and specific practices focused on building confidence, you can develop a learning environment where all students participate and contribute to rich mathematical dialogue. Once students experience success in mathematics, their progress will accelerate.
Back to Resource 11: Addressing avoidance behaviours in mathematics classes