For my style of learning one of the most effective days of in-class note-taking was March 10, when we creating a chart detailing:
1. The Population Parameter we would be calculating
2. The notation of the Sample Statistic we would be using
3. The name of the Sample Statistic we would be using
4. Any other facts about what we were calculating.
This was particularly helpful for me to see in the midst of learning about computing statistics relating samples to populations because it provided a one-stop shop for figuring out why we were doing what we were doing, to figure out when numbers we were going to be using, and how those numbers applied to our study overall. We used this chart-making process to ultimately show arguably the most profound notion we covered this semester, particularly in the last few weeks: that repeated samples vary, and as sample size goes up, (1) variability within each individual sample will not change dramatically, and (2) the variability of the means of the repeated samples decreases. So, ultimately, we created a chart to give us the basis for doing later work to show that, as sample size increases, variability decreases.
Throughout the semester we focused a lot of our work on figuring out if samples within two different populations would indicatively show us that those sample values extrapolated over an entire population would indicate a clear difference between the two populations in the quantity being studied. We first had to find an algebraic means of figuring out if two samples were significantly different from each other. On February 10 we finally got the answer we were looking for: if (the difference in the averages of the two samples) divided by the (average MAD of the two samples) was greater than 1, then we could say the samples indicated a significant difference in the quantity being measured between the two populations. This equation was later given some further definition, however, so we were not assuming (in)significance in a completely general sense. On March 26 we gave definitions to “Not Significant,” “Inconclusive,” and “Significant”:
• Not Significant: could be due to samples jumping around
• Inconclusive: we cannot tell if it is significant or not, but we do not know the reason why
• Significant: definitely a difference between the two samples
Some of the most effective collaborative engagement we partook in was our reflection on how we understood our GAISE report readings. In class or at home, we read a section of the GAISE report, and were welcomed to either take notes or highlight sections we thought were significant. The collaboration, then, came when we would discuss either with our table partner or our entire table what we understood to be significant about the reading. The discussion started with one person, Person A reviewing the reading. Then, Person B would paraphrase what Person A said. For the next reading, the partners switched roles: Person B would be the first to present their review, then Person A would paraphrase what Person B said. In this way both students would be able to understand each reading in their own understanding, and would also be able to gain the perspective of a peer.
One of the least effective moments of engagement for me were to very short Journal Jots that we did in class, specifically on the dates of January 27 and 29, February 3, and March 26. I understood the point of them: that we were simply being asked to write down our initial thoughts on an activity or a principle we had been working on in class. I did not engage in the activity much, however, because we rarely created dialogue based on those quick writes, so I never felt like we were doing them for any expressed purpose, and ultimately did not invest much thought into them. To get students more invested in the quick writes, I think it would be beneficial to allow students to discuss their initial thoughts on the prompt. Collaboration as a means of reflection is one of the key elements of learning in my experience, and students would likely relish the opportunity to share their intuition with classmates so they can see a different perspective on the classwork.
Another flawed engagement activity for me was the online blogging. Blogging, as an activity, is an effective method of reflection, to be sure. I just never felt like I knew what was required of us in our online blogging, such as when (if at all) we were required to blog online, and what the expectations of each blog was. Early on in the semester we were asked to create a biographical blog, which I did, but after that I did not create another blog. There were no rubrics or stated assignments that we had to complete via the blog, but I always felt like I was doing something wrong by not blogging. To stay more engaged in the continuity of the blog I perhaps could have motivated myself to transpose all of my Journal Jots onto the online blog, but I never felt any encouragement from other sources to do so.