A Second Dose of Standard Deviation
Lesson 10 of 21
Objective: Students will be able to gain experience in working with the standard deviation, how it connects to the bell curve, and extend these concepts to explain why the standard deviation of a population is distinctly different from the standard deviation of a sample population.
As the students enter the classroom, I greet them at the door and hand them a sticky note. While they find their seats, I make sure that the opening slide of the PowerPoint is pulled up and ready to go. I have the students write successes/struggles on their attempt at applying the concept of a standard deviation to the previous homework assignment. When they are done writing, I have them stick it to my whiteboard. As they come up, I look them over and begin to group them into similar-concept piles. Because yesterday was primarily focused on the motivation and background of the standard deviation, I expect there to be a lot of questions! Having the students highlight any success and failures helps me to personalize my lesson for the students. During the lecture, I can stop and pinpoint areas on the sticky notes. Sometimes when I do this, I even like to pause in the lesson and toss the sticky notes that we have addressed to the ground!
I have assembled a homework assignment that deals strictly with the mean, variance, and standard deviation of a population – not a sample population just yet. A few of the questions require the students to extend their learning, and justify their thoughts. I like to use this homework assignment as a measuring stick to see how well my students are buying into the culture that we are creating. I fully expect for them to have very detailed responses to the questions that they are asked to explain or justify! If this is happening, then the students are clearly buying into the culture with an emphasis on problem solving and reasoning; not just punching buttons and “doing steps” to get the right answers. If this is lacking, however, I recommend having an open and honest conversation with your students about what you are seeing and why a change in mindset needs to be made. They will step up to the challenge if the reasoning is explained to them because that is EXACTLY what we are asking them to do: explain their reasoning.