For example, this week was a 3 day week due to labor day was Monday and Tuesday was the first day of school... so my class did housekeeping stuff like review of the syllabus, getting textbooks, getting to know you activities, and (because we had time) I introduced the real numbers using a venn diagram... then I had the students make attractive posters of that could be posted in the room. Many of them were really good, so I posted in the room and gave those students an extra credit point. What a great way to start the year!
Other than that I taught two investigations: U1A1- Natural Numbers, Whole Numbers and Integers and U1A2- Rational and Irrational Numbers investigation. The natural numbers investigation is posted on the michiganmath.org website, but the site is still largely under construction... but if you want to download it, then you can.
I spent one day on U1A1 and two days on U1A2. Day one was fantastic! I really felt like I accomplished my goal of properly introducing students our brand of "mathematical" critical thinking. I introduced the topic with a "what do you Know, what do you Want to know and what have you Learned"... or KWL strategy. Next I went over the text portion of investigation with the students.
It is important not to spend too much time lecturing... our goal should to become the "guide on the side" rather than the "sage on the stage". For this investigation, no more than 15-20 minutes is necessary. The goal is to provide students with as many "looks" at the material as we can... students need to see it, hear and feel it. So it is important to give them information (and you can use a variety of strategies other than lecture to do this) so they see it modeled properly and hear it modeled properly. But, and this is the really important part of this textbook, you have to give students time to work on the investigation questions in class where you can guide them when they need help... thus, they know how it "feels" to do it properly before they practice independently.
These investigations are designed to such that most students can complete 80% of the material in class and 20% of the material at home. If I taught in a 45 minute hour, I would have stretched this out over two days and followed this 80/20 rule for assigning homework on the first night. Also, don't be afraid to give a "hand-waving" explanations of how to do what you anticipate as "difficult" questions.
For example, in this investigation, it is a good idea to explain to students about the modular arithmetic problems before you assign them the problem. Also, the terminology of natural, whole and integer can get confusing. Consider the problem that talks about fractions being integers or rational numbers... this is another good one to go over before you assign. This being said, however, it is not a good idea to explain all of the problems before they try them... allowing students the gift of figuring it out themselves will mean more to them than depending on you for answers. Our goal as teachers should be to wean them off of us... not make them dependant upon us (or should I say, us being co-dependent).
As for how the investigation went in class, I can say that I am pleased and we had a good start.
The reason I spent two days on U1A2 is due to the amount of longwinded explanation I gave of rational numbers. Apparently, I fell into my own trap! As the author, I can get caught up in every detail of what everything the text says. For example, There is proof of why sqroot of 2 is irrational. And although this is an interesting proof, it can easily be left to the student to read on their own time if they are interested. Again the real value of the investigation is that you teach students something and then you immediately give them an opportunity to use that knowledge and you constantly are providing them feedback.
In retrospect, I could have done this investigation in one day if i split the class into 45 minutes of introduction and practice with rationals first, then 40 minutes of instruction and practice with irrationals. Other than that, I was again pleased the format of the lesson and the questions students asked about how to do the mathematics. GREAT START... stay tuned.
No comments:
Post a Comment