When is it time to instruct? This is my concern right now as I prepare to enter the realm of the "new mathematics teacher". I know that I want to create a classroom were students are allowed to struggle, but when do I as a teacher intervene if the students appear not be moving in the right direction. If I do intervene how much intervention is appropriate. By this I mean, do I suggest strategies, or do I modify the task. If I present the task in a different way maybe the students will be able to develop a strategy. However, once class has started and a task has been introduced is it too late to change the task, if the task given does not connect to students prior knowledge.
If I opt to give instruction is this counterproductive. Can I provide a formula, and learning still occur. This is a concern of mine. How do I develop certain concepts without providing formulas and step by step instruction. The real world context of problems can draw certain desired outcomes, but I am uncertain if this will be the case for every lesson. I am willing to experiment, but there is still some skepticism about this approach. Of course, I want to implement a teaching style that produces efficient learning, and constructivism is the suggested method. I just want to know, in the constructivist approach, is there room for teacher guided instruction.
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3 comments:
I think guided instruction comes in the form of questions that gets the students thinking in the right direction. Obviously sometimes you have to tell students what terms are and mean (they are not going to come up with the term integer on their own). I think that it helps to come up with problems that lead to a formula/equation. During refining/questioning you would lead the students into the formula/equation.
I agree that there are unsettled questions still. This is so planning intensive, that I am afriad that I will get busy with life and resort back to traditional ways or have weak problems that will not be effective.
Deep breaths, ok? I worry about the equation part myself. I really can't see how a kid will just come up with y=mx+b with enough questions. But I think as Heather said the key to redirecting is definitely asking the right questions. I don't think you should change the task in the middle but suggesting a different approach I think is ok. Like 'what if you work backwards, would that help?' Or 'I see what you are saying but considering the question/task should be more focused on this other part?'
Don't worry, I believe in you.
constructivism, and deep breaths as well, is not an approach but an explanation.
I think you can use guided instruction. But all instruction is guided. okay, a copo out but let me say that the question is: what happens when you lectture and/or use guided instruction, or give formulas...the answer? they still construct.
Use whatever method you need to 'see' what they construct.
My advice: don't just give formulas cheaply as a practice. if students can develop or see how it is developed and related to strategies than try and have them explore.
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