As we have gone through Alice we have seen the need to just pull alot of practice problems for each of the rules. I still have students that approach these problems in a variety of ways. At this point there are some that have memorized the rules. I still have some who use expansion . I have explained to them that expansion is not always feasible but hopefully being able to expand problems correctly will help them to remember a rule.
Yesterday I spent the majority of class answering questions and going over examples from a couple of worksheets that I had left for them to work on when I had a sub. We have developed all the rules they needed throughout our Alice lessons but these problems had more "moving parts" for them to work through. After changing my teaching methods this year yesterday was such a "drag." I asked the students if they liked working through the packet instead of the Alice activities and some of them said yes. Today (while we were working through an Alice activity) I asked them whether they would prefer me just tell them the rule and give them practice problems or allow them to explore their way through a problem and help me to develop the rule. Once again I had some that preferred both ways. HOWEVER, when I asked them which way do you think might help them to remember the material 2 weeks from now not one student chose the "worksheet method." I think we will always have students that battle with you over having to think for themselves. There are many times that my students don't actually get ALL THE WAY to the rule or formula or method that they need to do the algebra. However, once they have had some time to "productively struggle" with a concept our discussion is so much more MEANINGFUL than when I just told the students the rule and had them practice problems using it.
One of my first major AHA! moments came when I attended an ACT Quality Core workshop in which Roy Dean was one of the presenters. I actually had to look back for some email communication between me and Roy in order to get his name. This was the first time that I remember sitting through a workshop (I hadn't attended AMSTI at this point) where MATH teachers modeled how to use strategic teaching strategies. He was very patient with me because I was often picking his brain about how he did things in his classroom instead of doing the actual activity assigned. When I found the emails I just wanted to share them because I learned so much from his answer. Below is the email I sent to him:
Thanks for the information and your willingness to share. So...when I
came back to school and started telling other teachers about the
movement to teach using the methods we discussed I often get the same
question. Teachers wonder if the group work translates into higher
test scores since the students take the tests (standardized - like
EOC, ACT, etc...) by themselves. Concerns are also expressed about
having students in our classrooms to learn primarily through the
methods we discussed when most college classrooms are going to be
lecture based. I didn't want to ask these questions at the workshop
because I feel like they seem argumentative. However, I wondered if
you have any direction or advice on how I might answer these
questions. I certainly share their concerns and understand the
I have pulled out the "On Course for Success" book and am trying to
skim it to get answers...but I wondered if you could give me some
Etowah High School
And here is his reply...
Sorry it's taken a couple days to get back to you. The severe weather yesterday had me "enjoying" the Bham airport for most of yesterday.
In answer to your question, I know the "on Course for Success" book has some data that you can use. I would also think if you Googled reform math scores, group work and test scores, and such if you would find some data on your questions.
As far as my personal experience, at my school our scores rose 6 points (a statistically significant rise for Colorado testing) the first year and 2 to 3 points over the next 8 when we switched out curriculum to a group/problem solving approach to mathematics.
I also had a summer school class (not exactly your star students) that I taught with the reform/group/prob solve math for 6 weeks in the summer instead of the usual fraction ws, decimal ws, etc. The students seemed to enjoy the class more. Of the 24 students I had that actually attended thes ummer classes, 23 improved the test scores the next spring and 8 moved from unsatisfactory to proficient (we have unsatisfactory, partially proficient,proficient, and advanced) and all but one improved their scores a substantial amount.
As far as students to college, students that returned from college to chat mentioned that the college classes were different (having more lecture) but they weren't hard. It seemed to me that since they knew the concepts and not algorithms, they could adjust.
Sorry I don't have any hard data for you. I at least hope this helps some.Thank you for your hard work during the training. Have a great rest of the year.