1) One of the examples that were given in this article was that in Japan, teachers ask mathematical questions differently than we ask in Canada. They ask their students, "in how many different ways can you solve this"? This question is inquiry based and can very well be used in secondary-school mathematics learning. However, the rest of the techniques that John talks about such as, asking a genuine question instead of asking as telling and not asking as asking; I will not consider them to be helpful to encourage inquiry-based learning because they are not prompting a thought process that is initiated by the students themselves. In this process, there is a big role that the teacher plays hence not really inquiry based learning. On the other hand, where John talks about intervening when the student is stuck on a problem and knowing when to intervene and how often to intervene is a great example of inquiry-based learning.
2) I had a really good short practicum where both my FA and my SA's were really happy with my first lesson. However, one of the things they told me that I need to work on is "asking questions". According to them I ask too many questions by probing them too many times. I realized right away what they were talking about and I had to fix this about my teaching. As John mentions in his article that asking as telling may not be the most efficient technique which I completely agree with. However, the biggest change that I am going to make in my unit plan after reading this article is by adding things like, "how many different solutions are possible for this problem?" or "what do you do when you get stuck" and have problems on my lesson plans where the most students will get stuck. Also, the technique of the teacher getting stuck him/herself is really impressive which I will try to use during my long practicum.
