Something I learned today was ________________________ (be specific! An answer of math is too general)
An example of this is ____________________
If I made a problem for a test using this concept it would be:
I tend to ask the first question a lot for reflection, for a few different reasons. I am trying to develop student’s vocabulary, confidence and communication skills about mathematics. I want my students to be able to openly discuss mathematics, without worrying about how they describe things, what vocabulary they use, or even worrying about peer’s reactions to their thoughts. One way to start this is by scaffolding questioning so that students have a guided response (which feels safer to students), but I also want students to be able to transition from this scaffold as quickly as possible. One trend in my students the past five years is that everything they have done in math has been overscaffolded. Students who need no help with problems or those that needed just a little push in the right direction have gotten so much “fill in the blanks” instruction that they no longer have the confidence to strike out on their own with their work. One of the big factors that leads to this is the fact that with AYP and NCLB, there has been a push to get the students who score low on tests or those that are “bubble kids” extra instruction. Schools are trending away from providing extra opportunities for students who excel at mathematics- leaving it to the classroom teacher. While this type of RTI is a good change, many teachers also overlook these students to focus on the same subset of students in an attempt to increase test score ratings for their classroom. The fact the MN Department of Ed also put testing scores into teacher evaluations just compounds this problem. We need to remember that no child left behind also means not allowing these students to falter or become stagnant in their own learning.
I ask that first question often to get student’s own thoughts: raw, unprompted, pure. Seeing the growth a student takes over the course of a year in their ability to explain their mathematical thinking and strategies is great for both students and myself. If students struggle with the openness of this question I will ask them more guided questions individually as they come to me to check in with their reflections. It gives me a lot of insight on how students perceive information in class, what do they remember- what things actually make an impression. I tend to find those small things, a weird picture or joke- or even an untimely interruption of class, usually are the ones that students remember. Do I try to do that every lesson, no. I am a firm believer of giving students structure in class but also that if you do the same thing too many times, it’s effectiveness wanes. By providing a multiple approach to teaching (keeping an overall structure but rotating how material is presented, explored and practiced) I have found students to make connections and have more “sticky” moments that stay with them and connect concepts.
I ask the final question for many different reasons. I have found that students think of the concept with a whole different perspective when they have to design a problem containing the mathematics versus just manipulating the numbers to find an answer. Many students will design a problem and when I ask them to re-examine it, find that they did not address the concept they were intending. It also provides me with a good test or quiz bank of questions. I am assured that students will know how to solve the problem (because I typically have them share their problems as a warmup for the next day), and they take a different approach to solving problems designed by peers.
So what was something you learned in class today?