I generally have a 2:1 student to computer ratio, but I can often get enough computers for a 1:1 ratio on the days that I need them. Most days I split my students into two groups: a problem solving group and a procedural practice group. I call this the 50/50 classroom because two halves of the class are split evenly, focused on two components of our mathematics program. My classroom is set up so that these two groups are physically separated.
I dedicate an hour of class time each day to math. Every student will be in each group twice during the week. So if a student is in the procedural practice group on Monday she will be in the holistic group on Tuesday. Since we meet five times each week, I use one of those days to work on whatever I believe needs the most attention.
Usually this fifth day is spent addressing topics students are struggling with in Khan Academy. Sometimes I will put students who are struggling with a particular goal in Khan Academy into the horseshoe and we will work on exercises together. Sometimes I break the room into smaller study groups of students struggling with topics with a student who has already mastered that topic.
Figure 1 - Diagram of my classroom. The problem-solving group sits in the U-shape and does not use computers. The procedural practice group sits along the wall and uses computers to practice KA. I usually sit in the U-shape to facilitate discussions, but I will also walk around the classroom and address questions from students working on Khan Academy.
THE PROBLEM SOLVING GROUP
Generally, my time is spent in discussions with the problem-solving group while the procedural practice group works independently. Occasionally I have a student facilitate the problem-solving group discussions, which allows me to circulate with the students working on Khan Academy. The problem-solving group works collaboratively to solve in-depth problems. These problems may be related to a project or may be designed to introduce a new concept. These sessions are focused on discussion and collaborative work. The idea behind these sessions is to construct new knowledge and discover new ideas and ways of solving problems. Students are both practicing being mathematicians and learning mathematics at the same time.
In the inside group, I spend most of my time being a facilitator with an agenda. I know what I want out of the discussions. Sometimes there are new things that are discovered along the way that surprise me, but, on balance, my role is to highlight understandings that are revealed and nudge conversations in directions that will be meaningful and useful. In the inside group, typically students are given a problem set that they get some time to work on in class and some time to work on on their own. When we meet as a group, students present their solutions or partial solutions and we discuss them. Most of my strategies in this area come from an academic learning approach called problem-based learning. This approach is used in many schools but I learned of the approach and became fascinated with it after learning about how it is used in Exeter Academy.
Figure 2 - Certain activities work especially well with student facilitators. Here students are attempting to agree on solutions to a set of problems by sharing all of the different answers to a problem and then agreeing on which ones cannot be correct. The ‘correct’ solution is the one that no one can disprove. This is almost always the right answer but when it is not I address the problem later.
THE PROCEDURAL PRACTICE GROUP
The procedural group works on Khan Academy. Each student is working on a predefined goal tailored to their current skill set. A goal consists of achieving mastery of a certain number of Khan Academy exercises. These goals have been set up by me in advance, and an entire year’s worth of goals are available at any time. The work is self-paced and mostly independent, but it is not uncommon for students to form study groups. Collaborative methods have been established by students themselves, study groups or one to one tutoring is fairly common. I allow those students to set up a work area outside the classroom so that they can interact without disturbing others. Additionally, I sometimes have academic tutors available to help students. Students are assessed on whether they met a weekly time requirement and if they kept a written record of their work.
Figure 3 - When students are using Khan Academy to increase procedural fluency, they are only assessed on the time that they put in and whether or not they have kept a written record of their work.
Figure 4 -**A goal consists of achieving mastery in a certain number of Khan Academy exercises. Theses goals have been set up by me in advance, and an entire year's worth of goals are available at the beginning of the year. The work is self-paced and mostly independent. The goal above was used while working on a project that required graphing the motion of moving objects.**
In the procedural practice part of my classroom, my primary role is to know where my students are skill-wise. It is also my role to know how much effort they are putting in and to help motivate them to practice and to understand the role of that practice. If they are struggling with a topic and are not being proactive about it, I need to teach them how to be. I see my role as one that should fade throughout the year. For instance I might arrange a peer tutor for a student who is struggling with a topic the first or second time but at some point I expect that student to take an active role in addressing their own academic needs. I organize study groups of students who are struggling with a topic with those students who have already mastered it. I keep kids honest with themselves - are they doing the work, are they afraid to ask for help, do they need to develop the confidence to help other students, are they respecting the norms we have set up in our classroom. There are still times when I do a small group lesson or even work one on one with students. I make myself available after school four out of every five days to help students in small groups or individually as well.
Project Based Learning is an applied, dynamic approach to learning. Students are presented with challenges and work in collaborative teams, usually building deliverable which meet the requirements of that challenge. For example, last year my students built rockets in one project and solar cookers in another. The idea behind the projects is to allow students to learn the academic concepts involved with the deliverables they are building. During these projects I sometimes use Khan Academy and exercises to help students learn or reinforce content related to the building of the project.