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The problem involved mathematical equivalence (i.e., 4+5+7=__+7), which is known to be critical to later algebraic learning. In the speech-only videos, the instructor simply explains the problem. In the other videos, the instructor uses two hand gestures while speaking, using different hands to refer to the two sides of the equation. Students who learned from the gesture videos performed better on a test given immediately afterward than those who learned from the speech-only video. Another test was given 24 hours later, and the gesture students actually showed improvement in their performance while the speech-only students did not.

1. Tardy passes.  The picture below represents all of the tardy passes I have received all semester, along with passes to the nurse and passes to assistant principals for discipline.  That stack represents a lot of lost learning time, especially when you realize that these passes are written for a lot of the same students over and over again.  If learning was really valued, there would be preventative action taken rather then just letting students be late and lose valuable learning time.

2. Announcements during class time.  For the first four years of my teaching career, I worked in a district where it was in the contract that no announcements could be made during class time other than regularly scheduled announcements during a set period.  Consequently I started teaching not knowing the agony of having my class interrupted with announcements about homecoming, meetings, or sports cancellations, and then having student attention diverted to those topics rather than what they are supposed to learn.  I always hear about cell phones being a distraction to students, but random announcements that could have waited until another time (or be made in another way) during a class can be just as much of a distraction from the real reason students are in the building. 3. Letting students talk among themselves for the last 5 minutes of class.  I am known as the strict teacher because I believe in bell-to-bell instruction.  I only have 50 minutes a day to cause understanding in my students, and I want to use all of that time.  Some students and some teachers find this unreasonable of me.4. Pulling students out of class for things that are non-learning related.  This school year alone I had students pulled out of class to talk about sports participation opportunities and to do something for an extra-curricular activity that was supposed to be done after school.  I even had a student pulled out of my class during a test because another teacher simply demanded it.  Now, I'm not against sports or extra-curricular activities; I feel they are a valuable part of a student's school experience.  It's when they start to take priority over learning that I have a problem.

 When we add up the given rates, we get  1/5,  which is the rate that 2 Ahmads, 2 Kumars and 2 Calvins would work.  Unfortunately we do not have the clones.  We just have one Ahmad, one Kuman and one Calvin.  So we divide that by 2 to get  1/10  and this is their combined rate.  This means that they can complete  1  house in  10 days.