Putting students in control of their learning

In the last couple of years, I've worked to really clarify exactly what skills I expect my students to learn. The assessment system makes it crystal clear what skills students know and don't know. And then I realized: Oh wait - it's only crystal clear to me. Students focus on their test scores, and come in to retake and improve tests, but they really don't think about what mathematical content they need to develop - only what test number they need to retake. I still have a few students who insist on retaking skills tests even though they haven't done any work to learn the skills that they got wrong the first time. Even when this fails to produce the results they want, they still resist actually working with me to learn the skill.

I think that helping students really understand what the individual skills consist of, and what their personal ability level is on each skill, is really the next step. I want students to understand the connection between their level of numeracy and their success in mastering algebraic concepts. I also want students to make connections between their behaviors in class and their growth (or lack of growth) in the lesson's objectives. Finally, I want to provide students with greater differentiation so that all students can both feel challenged and successful.

So, I put all of that together into a new plan for beginning and ending class. Students will start class with a 10 minute Do Now that has three parts. Part 1 is a Numeracy Skill Builder that targets a specific elementary math concept that is either key to the specific lesson, or something that students have been struggling with. Part 2 consists of one or two algebra concepts that are the lesson objectives. These are broken into basic, proficient, and advanced levels. The proficient level is the form in which the concept will be tested on a skills test. Students are told to solve only one problem in each concept, at the level they feel most comfortable at. Part 3 is a multiple choice test prep question. The purpose of this is obvious, as we need to get students ready for state tests, ACTs, placement tests, and so on.

Students have 10 minutes to complete these problems individually and silently. No helping is permitted here (in general), because the purpose is for students to really get a sense of what they know at the beginning of class on their own. At the end of the 10 minutes, I show the answers so students can see how they did, but we don't spend time actually reviewing these specific problems. I quickly collect the papers.

We have the lesson. Ok.

Now, in the last 5 - 7 minutes, I hand back the papers. On the back, students complete the Exit Slip / Reflection. They are supposed to go back to the Do Now problems, pick one algebra concept, and try a higher level problem. The idea is for them to see how much they can improve in an objective over the course of the class period. So, even if they are only able to accomplish the basic level (when they couldn't before), they can see growth in themselves and feel good about that. Students who already could do the advanced concepts at the beginning of the class have a shot at doing a harder challenge problem, so that they too can push their thinking (my advanced students really like this).

I just started doing this today, so I don't have too much to report about it yet. It seems to have gone well, though it took longer than the 10 minutes because I needed to explain the process a few times until they all got what I was talking about. As it becomes part of the routine, I'll know more about what impact it is really having.

Here is the first one we did, in pdf and word formats.

I'd love to get any feedback on any part of this.

Edit
We decided to make the reflection portion into a progress tracker, instead of copying it individually on the back of each Do Now. This log will be kept in a binder in the class. This will allow students to see how they did in previous classes as they are filling out the current reflection. It will also be a very useful document for discussions during grade conferences.

What's the percentage of "adders-across" in Numeracy?

In the past, I've given diagnostics before a unit so as to be able to compare pre- and post-instruction scores. Now, in the spirit of differentiation, I'm going to go one step further.

The next unit is about adding and subtracting fractions and mixed numbers. On my diagnostic, I wanted to see what percent of the students are still "adders-across" (#25 down: snakes that are bad at math). That would be 68/80, or 85%. The remaining 12 students could all do the basic algorithms, but most stumbled on the more complicated mixed number subtraction problem.

So here's the plan. In each class, I will assign one of the non-adders-across (NAA) to an adder-across (AA), tasking the NAA to help the AA learn over the coming lessons. If I see that they remain on task during practice time, the NAA will not have to take the quizzes, earning an automatic 100% on them. This seems reasonable, since they have already shown me they know the skill. Additionally, if the AA passes the quizzes (i.e. becomes an NAA!) then the NAA helper will earn some oh-so-coveted extra credit points. This way, the NAA has strong incentive to help, but there is no penalty if the AA doesn't make enough improvement.

Since almost no students showed mastery of the mixed number subtraction problems, every one will need to take that quiz when we get to it.

Now, the only thing that remains is to pair up the NAAs with the AAs effectively. I need to factor in personality, motivation, and so forth. Also, this experiment really highlights the imbalance between classes, even though we try to avoid any tracking (a constant difficulty in a small school). Here are the numbers of NAAs by period... Period 1: 5, Period 2: 4, Period 4: 2, Period 6: 1.

Software assisted differentiation

Is there anyone out there with experience using software to help differentiate instruction for students in math?

A couple of programs I've looked into: Aleks and Agile Mind.

I am interested in seeing if I can use something like this to help support my Numeracy students. Of course the websites are filled with anecdotal success stories and even data to support their claims of success. Has anyone reading this tried to use something like this? I'd really like to hear your experiences if you have.

Update:
Brainslug asks a clarifying question in the comments, and the answer is long, so I'm posting it here...

Short answer:
"differentiating" is edu-babble for providing different students with different instruction and/or assessment, as opposed to teaching the same thing/same way to all students in the class. Software might help with this greatly in my Numeracy class.

Long answer:
We have all of our students who test below 7th grade take our Numeracy class concurrently with Algebra 1. The problem is that skills range from around 2nd to 7th grade levels. Some kids need to work on place value and subtraction, while others are ready to tackle fractions. We decided not to split the class up into two or more levels to avoid the pitfalls of tracking in a small school.

So, to help students most efficiently, they need to be provided with instruction where they are ready to learn. One solution can be to split kids into flexible groups within the class, where the different groups are working on different skills. However, aside from this being an exorbitant amount of planning time, our freshmen generally do not have the student skills needed to work independently for long periods of time, or the ability to learn from static worksheets without direct instruction and good coaching.

The software that I mentioned above assesses students' "knowledge space" and then only lets them work on the skills they are ready for. The software provides explanations, examples, feedback, and so on. It also allows you to easily provide individualized homework and assessments. In my ideal scenario, I'd set up the class as follows:

Each week (or so), a new skill in math is taught. At the beginning of the week, all students take a quick diagnostic. If they pass, they don't participate in the lesson: they use the time to instead work on the software, on whatever skills they are currently building - plus, maybe some other problem solving curriculum. If they don't pass, they spend half the class (which is an 80 minute block) working with me on the lesson as normal: direct instruction of conceptual and procedural understanding, manipulatives when appropriate, and pair/individual practice. They would then spend the second half of the class working on their individual objectives via the software.

If this works, it would allow class time to be much more efficient, as students would only ever be working on material that was needed, and at the appropriate level. Of course, this all hinges on the software being able to make good on its promises. I'm hoping that the software is both understandable enough and engaging enough that my students can actually learn from it. Computer based learning could be just like a glowing worksheet, or it could make good use of video, animation, interactive demonstrations, and so forth to really move students forward. So my question: has anyone tried this with students?