(Note: Each week in C&I, we have a reading on some subject and have to write an unstructured response answering the "lens" question and addressing some of the issues in the reading. I'll include the readings when I have them, but most of these should stand up on their own.

Chapters 1 and 3 of Integrating Differentiated Instruction & Understanding by Design)

Lens Question: What should students know and be able to do when they leave math class?

I don’t see curriculum design as all that big a deal. This is why God created text books. Even if I don’t much care for a textbook (and I’m not a fan of CPM), the outline of the design is there. I don’t understand why the reading didn’t mention textbooks and how they, for the most part, define the state standards. That doesn’t mean I won’t be setting priorities and skipping chapters, and of course I’ll be supplementing with interesting side material as needed. But a lot of the angst about designing curriculum seems misplaced. I have worked with dozens of students using as many textbooks. There are good textbooks and bad ones, but they all get the job done.

The only really really bad thing, in my view, are the classes that don’t use textbooks. As a tutor, I’ve seen the kids at a loss when they don’t have a useful single resource, rifling hopelessly through various worksheets with notes and explanations on them. I would refuse to work for a school that doesn’t use textbooks.

I understand that, as part of C&I, I will have to design my own lesson plan and so on and so forth. I have, in fact, designed my own curriculum for short term courses in US history and literature/composition courses. But as a part of teaching, the course design will mostly be done by the textbook. Teachers have to design ways of making the material interesting and accessible. But the subject matter is mostly done. I can, of course, decide how much I will cover of that textbook, but there again, I think the choice is obvious: I will set my course standards based on the knowledge the students will need to progress to the next step in the overall curriculum.

As far as differentiated instruction, I expect that students will enter the class with a baseine of knowledge, or the ability to acquire that knowledge in a short period of time. I expect that some of my students will have forgotten how to add or subtract fractions since they left Algebra I two years ago, but I also expect they will remember quickly with a brief refresher. I will not be bringing out the manipulables to help them master it for the first time.

I won’t go to extreme lengths to help students who are well-below the baseline competency needed because, as the reading points out, differentiated instruction must not include differentiated assessment. Students who lack the baseline knowledge will not be able to master the course standards in the time required, and therefore I would be obligated to flunk them. As a matter of integrity, as a cog in the great wheel of public education, which depends on some level of standardization among course work and assessments, I am bound to ensure that my students are assessed on an equitable standard--equitable, that is, to all students.

I see these issues as entirely separate from my commitment to individual students. As a teacher, I am committed to giving all my students a sense of competence--first as learners, second as students, and finally (and only incidentally) as mathematicians. I have been doing this for five years, and I expect to continue. While I don’t expect I will ever allow students to choose their method of performance, I will never fail a student who can do the work.

I have been much reassured by my experiences at HSP. First, just as I expected, we are essentially following the textbook--very little curriculum design is done by the teachers. We do things like decide how much homework to give them, and whether or not we’ll follow the instructions to “direct teach”.

While our students have entered Algebra II/Trig with varying levels of ability, we are successfully “upgrading” the students who started with less knowledge. While we were ready to recommend that students be put back into an earlier class, we have not seen the need to do so--but the fact that we have the ability is extremely comforting. Similarly, I am encouraged that we aren’t assessing students by different standards. In fact, I would probably be easier on my students than my CT is, giving them more leeway to demonstrate their knowledge and being less demanding that work be shown in situations where I know they understand the material. I am less committed to the math than I am the learning, the demonstration, and the competence. If a student knows how to do the work but doesn’t understand the question, I have no qualms about giving them more information about the question. At the same time, I am uninterested in whether or not students who manifestly know how to do the work actually show their work. Fine with me if they did it in their head. The students I want to show their work are the ones who aren’t clear on how to do it, so they can get a better idea of how to work through a problem and show their thinking. But insisting that kids show their work even when they can do it in their head is a bit too moralistic for my liking. Thus, while my values and expectations differ considerably from those outlined in the readings, they seem pretty much in line with what I am finding at my placement.