Sequences and Series and Differentiation

Things are moving right along in my 10th grade classes. We wrapped up the Stats unit with some really fun individual research projects in which students created a question about our school community that they wanted to answer, collected data, and performed either chi square or z-tests to answer their questions. I was really, really happy with the level of work students put into their projects and how much ownership they took over their learning.

Here is a picture of the summary slides I asked them to create to summarize their research questions and conclusions. It was really nice to be able to display the results of our labors to the school community.

We started working with sequences and series. This is a relatively short unit and I am pretty happy with the unit projects, which were due last week. Students needed to create their own visual pattern, write recursive and closed form rules for the pattern and its differences and sums, and try to prove one of their formulas using induction. That last part proved really hard for just about everyone. Maybe it's because I haven't really taught proof by induction before, but it was just a painful slog for everyone involved. I have no idea how to teach it in a constructivist fashion as it seems so far removed from the way that most students would approach a proof.

The other challenging part of this unit for me has been appropriate differentiation. For several students, writing rules and finding patterns seemed intuitive and they flew through classwork problems, while others have really struggled and I could tell they needed more support. Most of what we do in class is groupwork based, which has its advantages and disadvantages in terms of supporting struggling students. They can get help and work with peers, but they can also chill on the sidelines and rely on others to do most of the work. I do call on random group members to explain the group's work, but this isn't the same as actually doing the group's work. There is also a big discrepancy between students who are seeking me out for extra help outside of class and those who are avoiding me. Spoiler alert: it's not the students who really need the help who seek it out, for the most part. 

When I teach middle school students, I feel comfortable emailing home or just telling a student that they are required to work with me during lunch or before/after school. For high school students though, it feels overly babyish to do this. I want them to have independence and learn to reflect on their understanding and ask for help. Conferences were a great time for me to communicate to students what I would like to see them doing differently, but the challenge now is to find the time to follow up with individual students and remind them of the commitments they made in their conferences. It's a tough balance between giving them freedom to make their own choices and mistakes and also coaching them in how to learn from those choices and mistakes. One thing that I would like to do is to meet with each student one-on-one right after Thanksgiving break to discuss their progress. As always, finding the time to do this is a challenge.