We all know students have access to apps and programs on the internet which will do the work for them. They put the problem in and the answer pops out. If they choose the right app or web site, the solution will include all the steps necessary to "show their work".
They get great scores on the daily work or home work but when the test arrives, they are totally clueless. This is something that will not change unless mobile devices and the internet disappear. So what do we do to make sure our students are learning the material.
I have seen several suggestions to help students learn the material while using apps to solve problems for them. Suggestions which fall under the heading of explaining their thinking.
1. Post two different worked out problems which are almost the same but just a bit different. Have students discuss the similarities and differences. This could be done either verbally or via collaborative technology.
2. Post a problem from the new material with all the steps. Have students explain what is happening for each step. If they understand the material from the previous section, they can build on prior knowledge.
3. Post a fully worked out problem and have students write in what is happening with each step, much like the the examples in most text books.
The idea behind having students write out the explanations for each step is actually two fold:
First, it is a way to access student understanding of the material. If they cannot write explanations of the steps, it means differentiation and scaffolding may need to be implemented.
Second, it is a great way to monitor student thinking and identifying misconceptions.
As teachers we've reached a point where students need to know more than the mechanical steps used to solve a problem. They are required to understand the mathematical reasoning behind solving problems and they have to know how to explain their own thinking. This is a complete paradigm shift from even 10 years ago.
So to ensure this, we must change our expectations and our methods to help students learn to explain their thinking. I'd love to hear your thoughts on this.