If your cake is not cooking in the middle, then pop it back into the oven and cover tightly in tin foil. The tin foil will trap the heat and help to cook the inside of your cake. Bake for another 10-15 mins checking after 5-7 mins to make sure it's working.
It's happened to me. I learned to use a toothpick, knife or cake tester (thank you pampered chef) to monitor if the cake is done. It's really an easy way to formatively assess whether the cake is ready to leave the oven and become 'proficient'.
We often are puzzled why students aren't able to successfully navigate grade level math problems. Math is an abstract concept. When you are learning a topic, pure abstraction can be a good way to get lost. It helps to find a specific, concrete meaning for the abstract ideas. I challenge you to move students through these stages and when they get stuck or seem to not understand look toward concrete to insure understanding.
If you want students to 'learn' and 'understand' you need to make intentional decisions that are based on student work. Don't rush; use your instincts and choose to bring manipulatives in when it seems that kids aren't being strategic. 
- Concrete “doing” stage: Make sure you spend time here with student evidence of solid understanding. When you have a few students who may not 'get' the math. Differentiate and give them manipulatives to use while other students move on to the next stage.
- Representational “seeing” stage: The resource takes lessons here quite quickly. When you find that you are explaining more bring in manipulatives as a scaffold to support transition.
- Abstract “symbolic” stage: Clearly this is the quickest and most efficient phase. However, kids can not move to automaticity without concrete and representational understanding. Simply memorizing will limit how they use strategies.
The cake needs more time.
I agree that students need us to not rush, that they need time to use manipulatives & work on problems. My questions is, how do we do that & move so quickly through material in Bridges as the same time. They seem to be opposites to me.
ReplyDeleteThis is not easy to do, Paige. One idea is to lessen the number of problems students are expected to complete. If they are using manipulatives and we're anticipating it will take them a bit longer to solve problems in a concrete way, then we can adjust the amount of problems they are practicing with. The key to using this idea is looking at the work students will do ahead of time and purposefully choosing which problems you want all students to solve, and which ones students will be able to complete if they finish the required problems.
DeleteAnother way we can support students with this is through Math Intervention time. Several times a week during this structured time, we can give students opportunities to explore and solve problems with concrete tools before being exposed to lessons addressing the same concepts through core instruction. This is where I will be supporting the 5th grade team!
I totally agree - sometimes they just need more time! As time passes, it seems like our "resource" and "road maps" are rushing students through the material and there isn't time for mastery. This year has forced me to branch out to pick the minds of other experts who use the same resources. Everyone is saying that it's too much for students to do and notice that mastery isn't happening either. We CAN'T keep sprinting forward HOPING the spiral will catch them because it feels like we're having to reteach more and more. The tin foil (aka intervention) can't save them all from under baking. Sometimes you have to go slow to go farther...hopefully our fearless leaders will see that again SOON....before too many leave us underbaked and still gooey in the middle.
ReplyDeleteThanks for addressing this, Kim!
ReplyDeleteStudents do need time in the concrete phase of learning, especially when first being introduced to a concept.
Something to keep in mind is that the amount of time they need to spend in this phase will differ with each student.
I really appreciate when you brought up the phase that comes between concrete and representational, when students are making connections between the two: "When you find that you are explaining more, bring in manipulatives as a scaffold to support transition." Seeing the connections between concrete and representational as well as representational and abstract can be so automatic for us as adults and teachers that it can be easy to assume this connection is obvious to students, too.
Investing time to have students analyze the similarities and differences between each of these phases is critical to developing their mathematical understanding.