Assumptions:
- Administration will support this model. It can be integrated into "the system."
- There are many ways to demonstrate mathematical "smartness."
- Students will cooperate with this system.
Things I Agree with:
- "Learning is not the same as achievement" (p. 12). My biggest fear (okay I'll be honest, it's an unfortunate reality) is that this is the truth. Do the grades of my students necessarily match up with their understanding? Or is it their ability to memorize what they need to know for a test? Is it their ability to cheat and get the right answer? Some students' grades are higher than their level of understanding; some are lower. I try to be as fair as possible in remedying this, but sometimes there's more doubt than you can give students the benefit of. This is why I strongly consider a greater implementation of SBG. Moreso, I want students to focus on their learning and not their grade. As Jo Boaler says in this video, math should be a "learning subject" and not a "performance subject."
- Establishing classroom norms and posting them: I think the norms of "Take turns, listen to others' ideas, disagree with ideas, not people, be respectful, helping is not the same as giving answers, confusion is part of learning, and say your 'becauses,'" (p. 28) create a really great structure for engaging all students and creating a good classroom culture.
- "Start with challenging stuff, not easy stuff" (p. 39). I saw a clinical student of mine successfully do this, when I was really skeptical of how it would work out. The engagement was at a very high level, and the students put in really great effort. I was afraid that they would quickly disengage because they wouldn't know what they were doing. Now, three students were extremely disengaged, but I wonder if this could have been helped with more structure and the use of norms in place. This is going to be another substantial shift of my practice next year.
- Peer observing: positives and questions. I love this. I love "questions" instead of criticisms. It is so much more nonjudgemental and I think helps the teacher reflect without feeling threatened. I also agree that starting with a positive is a good idea. Sometimes observers are so concerned about helping people improve, they miss the opportunity to set a good tone for discussion and reflection. I also think about this in giving my students feedback. Do I start with a positive? Do I ask them questions to help them reflect on their learning and improve, or do I judge too much? (Full disclosure: I judge students too much, and I want to make a conscious effort to change this.)
Things I Argue with:
- "Mathematics is not hierarchical." I can understand how ideas can be connected, but simply speaking, people don't learn to run before they learn to walk. A lot of math is based on structure and repeated reasoning, and while I can see the need to apply ideas to different places, in terms of math for the sake of math (which is still important!), you need to build on your prior knowledge. How are you supposed to add two rational expressions if you don't understand how to add two fractions?
- I might be missing the author's intention, but I wonder if the author is implying that although quick and accurate calculation is a type of mathematical "smartness," other types are also just as acceptable. I've gotten off the quick part. But, I think it is heresy to say accuracy is not important. Accuracy makes sure that the building doesn't fall down and that a patient doesn't overdose. Accuracy ensures that stockholders don't lose their life savings. While procedural skills are not everything, they are still important. Furthermore, some students will need them in future courses. It is not fair to these students to handicap them in future courses because they cannot carry out important procedures. We still need to require deep understanding of the math behind the procedures, but kids do still need the skills. Although it appears sarcastic and exaggerated, I think this blogger brings up a very important concern in this entry and this statement he makes in the comments: "It's all part of the 'multiple ways to be smart' or 'assigning competence' process of CI. So Juan can't add, but he can explain the group's solution. Sally can't multiply, but she can draw the poster. And so on." I'm sorry, but Juan MUST be able to add and Sally MUST be able to multiply. Being able to explain a solution does not absolve a student from being able to do the problem correctly. Skills are still important.
- "Watch your pace" (p. 90). If you can get your entire department on board (and maybe entire country????), this sounds great. Reality doesn't sound so great. In reality, the Common Core and the PARCC now say that students will be tested on this list of standards at the end of the year. Furthermore, my livelihood might depend on this. How can a student do something he has never been exposed to if we haven't covered it? Secondly, math courses in the United States are mainly hierarchical. If a teacher in a future course expects students to know things from a previous course that they don't know, then the students are at a huge disadvantage. Finally, the "we shouldn't move on until the students are ready" might be pedagogically sound, but it also takes responsibility off the student if the expectation is "I don't need to put in any extra effort, because the teacher will just go over it again." How does that foster students' sense of ownership and responsibility? (Separate post about this issue to follow later.) In theory, I really do "agree," but I have a hard time getting it to work within the reality of "the system."
Things I Aspire to:
- I aspire to make my classroom a place of positive interdependence, where students can take ownership of their learning, and I don't get in their way.
- I aspire to have all students, even the reluctant learners and low-performers, to be engaged and to always put in their best effort towards understanding and continuous improvement.
- I aspire to implement classroom policies that support math as a "learning subject" rather than a "performance subject."
- I aspire to make sure that even while working under a Complex Instruction framework, students get the skills they need to be successful in future courses if they need them.
All in all, I think people would gain a lot from reading this book. The ideas are really helpful to find and design engaging lessons and create a good classroom environment, especially as many schools are using the Charlotte Danielson framework for teacher evaluation. Some of my lessons don't go well because they need more structure, and I think some exceptionally good structures are provided in this book. Furthermore, the book is very helpful in trying to find ways to work with a wide range of abilities of students. Our school is dropping low-level classes next year, so almost all students will be together.
I am left with two big questions after reading this book:
1) Will this really work? Or, even after assigning competence and explicitly stating that all students need to be ready to answer, but even a partial answer can be helpful, will kids continue to insist that "I don't know" when I'm asking them a question that they have no excuse not to answer, and the class is just sitting there waiting because I want to make sure I'm using appropriate wait time and still holding the student accountable for answering but the rest of the class is getting fidgety because most of them already know the answer?
2) Ideally, there would be no "honors" classes either. How do you use this structure to differentiate up and teach different levels within the same class, especially if honors-level students need extra skills for their future courses (e.g. "honors algebra 2 skills needed for calculus but not necessarily needed for the algebra 2 kid going to art school.)?
