I think it is true that students see making a mistake in a very negative light-they can look crushed if they have got something wrong. I think it can be a challenge to turn that round in the upper primary and I think it is a challenge teachers in the earlier years need to rise to- teaching children that mistakes are part of learning. Parents do get the idea though that you are saying it's OK to mke a mistake and not really care about that so there is also a challenge to ensure that the message is that mistakes are OK as long as we work them through. I guess this is linked the second idea in the session around persistence.
The idea of the Didactic Contract was new to me. In some ways it reminded me of the constuctivist idea of scaffolding learning but I guess the message here is that teachers can 'over-scaffold' in order to help students get to the 'right' answer.
I was interested to read more about the role of 'speed' of calculation in Maths and I think many people do think that those that answer quickly are better at Maths. The idea of that being quick with an answer means you are 'smart' is one that resonates with me. I am a slow processor! I like to take my time to think things through. I like to read things at least a couple of times before committing to an answer or an opinion. I think it is so important to give students time and to make sure that those with their hand up first aren't always the ones we pick on to answer- this relies on mindful classroom management.
I connected to this lesson's emphasizes the importance of making mistakes, reflecting on them an having the persistence to try again. It rang very true that parents and peers often put pressure on a student to get things right the first time and teachers feel pressure to help children who ask for it instead of letting them struggle to work out a problem on their own. I had never thought of the idea that students and teachers might be in a contract that was potentially detrimental to student learning.
ReplyDeleteThe number one thing I would like to make sure I have established is a community in which mistakes are allowed without negative feelings and even encouraged by peers as a way to help them think more deeply as individuals and as a group. As and educator I was thinking about how often I call on the children who raise their hand, how often I give enough time to think, or call on someone who isn't raising their hand.
I do feel extremely fortunate to work in a school were testing is not a priority and discussion, explanation of one's thinking and collective ideas is held in high regard. The ability to work with students on their skills without a need to give them a speed test or measure their worth by a standard score is very freeing.
Making Mistakes
ReplyDeleteI really like the idea of celebrating mistakes and seeing those as a vital part of learning, not only from the brain growth perspective, but also in developing attitudes around perseverance, creativity and power.
Perseverance in trying multiple ways to solve a problem and having a go, even if it might not work out, is an attitude that is obvious when children are involved in play such as building with Lego or solving social problems on the playground. I am wondering how to transfer some of the play attitudes, to maths in the everyday. It is only when an idea is born and persistence in trying multiple ways to solve problems during the evolution of an idea, can the new ideas become reality. In my view, this is what learning is about - persistence in, and experiencing misunderstandings as well as the self doubt that is part of the learning process.
Challenging for me, will be to change mindsets (including my own) on what it means to be a successful maths student, as one that shows perseverance through the uncertainty inherent in solving problems, trying things out, being creative and making mistakes. This will be an area for reflection in my teaching. Key questions – how do I create a classroom environment that is stimulating for children to persevere at a task and enhance creativity? – how can I create an atmosphere of maths play that provides deep understandings? Lots to think about!
I have always struggled in maths lessons in my own schooling because memorising facts was not a strength of mine. I struggled with trying to understand formulas and algebra without a deep understanding.
The idea of having time to understand a concept and engaging in mathematical reasoning with others as well as celebrating mistakes so that all can learn from them, makes so much more sense.
Mistakes: We've been told that there is brain growth when somebody becomes aware of their mistake. I wonder if the brain growth is different for somebody who finds their own mistakes and somebody who has their mistakes pointed out by somebody else, or if it's only dependent on whether they have a fixed or growth mindset.
ReplyDeleteI think the teaching emphasis should be on supporting students in finding their own mistakes, helping them to become independent learners in a growth mindset culture where mistakes are valued.
I wonder at what point a teacher or peer should help out by showing students where they've gone wrong with a piece of work.
If students aren't making any mistakes, we should be providing them with more challenging work to give their brains an environment in which they can grow.
The didactic contract: I remember certain students who seemed particularly skilled at exploiting this contract. They'd say they couldn't do the work, and just sit there. In an attempt to help, I would break down the work further for them, and do some as an example. Often this would not be enough. I'd come back later to find no progress, so I'd help a bit more. By the end of the lesson the feeling of pressure to help the student with the work and the limited time sometimes meant I did most of the work for them. When I changed the game and said if they couldn't do it now they could stay in at break to work on it, the student miraculously found they could do the work after all.
I think in a problem solving environment where students are often encouraged to choose which problem they will work on the didactic contract is rarely seen.
A hypothesis culture: We want to create an environment that values problem-solving, mathematical play and exploration. For students to be able to try new possibilities, they need to be able to see new possibilities to try. This requires dreamers, those who will play with ideas and view them in new ways. It requires perseverance and to learn from trying. It also requires time. If teachers are insisting on finished work and correct answers to the questions they've set, this type of environment won't flourish. I'd like to create an environment where students propose mathematical hypotheses and then try to prove them. In Session 3 Part 18, the second question focuses on the generic, whilst the first is only concerned with a specific example. I'd like to encourage children to think about the generic. Can they propose a hypothesis and prove it? Maria talks about encouraging students' creativity in math, and I think this is one way we could do this. It's not only the teacher that sets out the problems, it's the students who come up with interesting questions to explore further. For example, whilst I was subbing last year some Grade 4's came up with the following hypotheses: If you square an odd number, you get a number with 3 factors; Anything with a 6 digit will have 4 factors; If you square an odd number, you get a number with 3 factors. Interesting proposals ripe for further inquiry!
Speed: I connect to Dawn's comment about making sure we don't always ask the students who have their hands up first. There are many strategies to give all students time to think - pair share, writing answers on white boards, using name cards to decide who will answer. It's interesting that time pressure in a math test often adds stress and anxiety whereas if students self-select a game situation the time pressure can add to the motivation. We need to remember that whilst games can be great for learning basic number knowledge, math is mainly about applying the knowledge in a variety of problem-solving situations without time pressure.