When I first started teaching, this was my math lesson cycle went; manipulatives, maybe a cutesy foldable, basic computation, word problems, and real life application. (And by including real life application what I really mean was a rushed word problem if there was time and usually only for the learners who have mastered the basic computation.) But this approach left only served about half my kids. It left another fourth of them snoozing from boredom and another fourth still unable to choose the correct computation when given a word problem.
So How Did I Fix This?
My first step was to bring real life application to the forefront. I adjusted the problems in my curriculum so they have my students' names in them. I re worked problems so they became things that could really be done in my classroom.
If I was studying area, I have students "tile" a wall. When we studied temperature, I had my students build coolers or solar ovens and see which temperatures and designs were the best. I found that the hands on approach got all of my learners interested. Yay! Right?
But What Did That Mean for My Lesson Cycle?
Well, it changed it quite a bit. And I won't lie to you, it was an adjustment. Before I whip out manipulatives or computation practice, I start with a problem or an event. (Something like tiling.) I would let the students read over the problem and start a Know/Need to Know.
"Knows" are the details that we know from the problem OR things that need to be done. (For example, the students might know they need to tile an area. Next, they may tell you the dimension of the area to be tiled found in the problem.)
"Need to knows" are the things that they have to figure out. (These are words you purposefully embed into the problem and what the problem is asking you to find.)
After we finish asking knows and need to knows, I turn my students loose on their problem. (At some point before we started the unit, I've already given them a pre-assessment with basic computation. So I know where they are as far as basic skills before we begin the problem.) I let groups talk about what they need to do in order to solve the problem.
While the groups are talking, I walk around and ask questions. Sometimes, the groups take off and have enough foundational skills and knowledge to hep begin the problem. But MOST of the time, they don't have a clue about where to begin. After I ask some pointed questions, they ask me to teach them how do something!
By about half way through the year, the students started going back to their tables and coming right back with a new need to know. They were identifying what they needed instead of me spoon feeding each step!
After you start with the problem, what next?
Before starting a unit, I prepared my lessons like normal. That way as the problem progresses, I could whip out mini lessons when they are needed. Each of my groups may or may not be in the same place throughout the problem so I don't always teach whole group. I often did small groups or guided math. Which means you need to be prepared to teach whatever your students may need. (Again, with that handy dandy pre assessment, there really aren't too many surprises.) During one math lesson I may have students watching videos for further instruction in basic computation, be teaching a guided math, or guiding a discussion about problem solving with different groups.
All the while, I've met a variety of students' needs as they solved a real world problem.
In this approach to math, the lesson cycle is more like a knot. All the pieces are daily being weaved into the project. I pull out manipulatives no matter where we are in the project. Assessment and guided math are constantly occurring. We are tackling problem solving skills as well as computation skills in complete integration.
At certain points during the project and at the end, my groups present their work. They must share their thinking, adjustments, and final product. Next, I have them write a reflection. Finally, we move/discuss the need to knows and place them under the "knows".
This approach to math may feel chaotic at times. But the students develop a depth of understanding that is incredible. It allows for intervention and advancement in so many ways. (But that's another post for another day.)
Have you tried problem or projects based in your classroom? Have you done anything that you think really works in teaching math?