Student Observations
Below are examples of the feedback forms that are written for EVERY session. Next to the sample forms is a description of their contents. They contain notes about topics covered as well as important information and recommendations.
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These are real examples from sessions with real students. The names and dates have been changed and the handwriting is computer generated.
The forms are written on 5.5" x 8.5" two part paper. The family is given the yellow copy at the end of each session.
Here is an example from a session with a 6th grade boy. He was just starting to work on substituting for variables into algebraic expressions.
He was confused about what to multiply by when there was no coefficient in front of the variable. It was noted in the feedback so that should his parents need to reinforce this later on they can use the same terminology and explanation.
We worked on establishing good habits early on when substituting for variables. He was surprised by the suggestion of using parenthesis because his teacher had not told him to do so. Rather than rely on the "Because I told you so!" method he was shown some examples of when the use of the parenthesis helped in the prevention of errors. It is always best to be able to give students concrete examples or proof of why they are told to perform a task a specific way. One of those examples was included in the feedback so that the student and his parents would have an example to reference if needed.
It was recommended that he is encouraged to continue to use the parenthesis when substituting. It was assumed that since his teacher had not yet recommended doing so that it was not going to be soon. Knowing how important a technique it will be in the future it is worth recommending. The remainder of the recommendation is a reminder of things that had been previously discussed that still require more work. Neatness and organization are always skills worth working on.
Here is an example from a session with a 11th grade girl taking Pre-Calculus. She had just started working on polar coordinates.
As with many students, she likes to know the "Why" of what she is doing. We spent some time discussing casually why polar coordinates were implemented, what they work best with as well as relating them to what she had already been taught about vectors. Showing her the interconnected nature of mathematics helps to cement a greater understanding of what she is doing. When she can see that polar coordinates are just a coordinate system for the application of vectors she can bring all of the knowledge she has about vectors and how to manipulate them to the problems she will see.
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Strict memorization has its place, but for many things it is possible to show the students how to derive formulas on their own. Not only is this a great way to teach the formulas and to show even more interconnection in mathematics, it is also a useful tool as a fail safe if the students forgets the formula on an exam. The feedback here shows the parents a basis for how to assist their child to continue to think in a more global way. It is also a refernce for the student to look back to if she does forget the formula. She can look and see that we derived it ourselves, and that will spark her memory to re-derive it.
It was recommended that she continue to draw small diagrams. These are useful tools to be able to visualize problems as well as to see solutions when calculations lead to undefined results.
