Interesting project. Did students in the control classrooms have other types of hands-on and engaging opportunities to explore the same mathematical content?

Interesting indeed!

I was struck by what I think i understood to be referred to as " lecture through activity-based methodology" as description of the Control Group pedagogy. Did I get that right? If so, could you elaborate?

I’m also interested more generally in what differences were observed between CG and DG in terms of classroom instruction.

I’m also curious if you calculated a Cohen’s effect size. I understand that the effects were statistically significant, but ’m not familiar enough with HLM to know if they were large or small or somewhere in between at each of the levels.

Thanks!!

This seems like a really robust study – well done! I’d love to hear your thoughts on what key principles you would take from this project, to apply to other computer-assisted learning programs.

Hi Ben, I worked on the project and will share a tad until one of our official presenters can address your questions. I have some of the statistical analysis on my hard drive but I may not have the most up to date results and will see if someone else chimes in before I do so. As for the CG “lecture with activity” it is generally referring to what we called a “business as usual approach” based on their teaching practices already employed in geometry classrooms in the districts. They tended to use class time lecturing/leading discussions, and hands on activities such as with patty paper, MIRA, compass, etc. These activities were not strictly inquiry oriented but more so of the form: present new material, use a hands-on activity to reinforce, further understand/explore that material, verify the theorem/result through the activity. Given there were 30+ CG teachers and many school days, there was variation to this, of course. I think my description describes the typical approach.

Ben:
I am involved on the statistical side of the project. We did compute effect sizes for each level of the classrooms. In the school districts geometry classes were split into different levels depending on the Standardized Test scores of the students and parent wishes. The three levels we included in our model were: Pre-Advanced Placement (or Honors), Regular and Middle School Pre-Advanced placement. The Pre-AP students were typically, but not exclusively 9th graders taking geometry. The regular class was mostly 10th graders. The middle school were mostly 8th graders. Not surprisingly, the differences in achievement between these groups was very large (both pre and post). Middle School out performed Pre-AP which outperformed Regular. So we computed effect sizes within each group and found effects to be: Regular = .55, Pre-AP .27, and 8th grade =.19. We found these results to be quite exciting, since the DG group outperformed the control group in each of the three levels (though the effect was small in the Middle School level) and the greatest effect was in the Regular group. This is important because the Regular was the largest group of students and one could argue is the group that needs the most help. Furthermore, doing a item by item analysis of the results on the Post test, we found that DG effect was quite robust, meaning that the DG students outperformed their control counterparts (this is controlling for pre-test, teaching experience and level of the course) on nearly every item of the test.

This is very exciting. I have a few questions about the study. First,how many classrooms were in the control and experimental group? I am sure it is somewhere, but I didn’t see it in the video. Second, did you find that the teachers in the DG group had facility with the technology. I know we have found various levels of comfort with the teachers we work with. And if so, how did they adapt to the use of technology?

I was very interested in seeing this study and the positive impact of using dynamic geometry software on student achievement in geometry. I was concerned however, that a key finding highlighted here is that students in the DG condition were faster at proving. It’s pretty well established that, while fluency is important, focusing on speed does not foster the type of creative thinking and productive mindset in students that we want to accomplish.

Wendy:
Just to piggy back on what Sharon was saying. The issue of speed had to do with semi-structured tasks where teachers (and separately students) were given new geometry problems to explore. The goal was for the participant to explore, conjecture and then prove their conjecture. In the control group the participants were given ruler, compass and protractor, while in the DG group there were allowed to use GSP. The interviews, which occurred at and during school, had a time limit due constraints of the school schedule. In this context, the DG participants were able to explore more cases more quickly and then move to making a conjecture. With the added time and help of the software, they were able to test their conjecture and in most cases prove the result. The control participants, who were restricted to classical tools, also tried create examples and explore the problem. However, the tools slowed them down. In some cases, they were unable to use the tools to construct an accurate figure which impeded their progress. In this sense, many did not have time to reach the level of proof. This of course was related to limited time. However, the sense of progress being made using GSP also provided motivation and momentum to the DG participants.