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Anonymous wrote:Thank you for all the responses. Even the ones that just called me a troll and told me I needed help. I see I jumped the gun but this is new for me. This is my only child. She has always excelled and seeing such a low score freaked her out and it freaked me out. I did not know what my options were and it was disappointing to learn office hours can't start until a certain date, even if a child needs help. We will look at daily Khan Academy as a tool (great suggestion) as well as finding a tutor. She seems to struggle with planes when there are multiple ones involved and intersecting. She got the "always" "sometimes" "never" questions wrong. One question was "Two intersecting lines are ______ coplanar" and she put "sometimes." Stuff like that she got wrong. I don't know if that is a vocabulary issue, an issue understanding planes, or what but we will figure it out and help her.
what kind of garbage test is this
+1
Huh? It is a fundamental question on understanding geometry. Intersecting lines always have to be coplanar. Think of a box with one edge that is the length of the box on the bottom (let's say one of the edges that touches the ground if the box is on the ground) as one line. In order the edge of the width of the box to intersect it has to be one of the edges on the ground as well. If it is the width that is on the top of the box they wouldn't intersect. They would be skew lines and NOT coplanar.
If you can't understand that concept honor geometry is going to be really hard.
um, the problem is not that this is too hard but that is too easy. a person who merely learned this by rote can answer it correctly without knowing anything.
It isn’t too easy since OP daughter missed it. It is a different way if thinking about objects in space.
The issue is these types of questions (always, sometimes, never) are terrible test questions especially this early in a class. For both reasons, on one level it requires complex thinking that I don't think should come week 1-3 but on the other hand, it is a thing someone can memorize and not even grasp. I have no idea what OP's daughter should do. Soumds like she has a bad teacher but such is life. This may be a class she has to retake in 9th or the teacher stops giving stupid quizzes and the child knocks it out the park.
I agree that this is definitely not a good question to pose this early in the class, especially if the students have not discussed planes in space, namely the axiom that three non-collinear points in space uniquely determine a plane (this is the 3D analogy to the axiom in 2D which says 2 points uniquely determine a line passing through them). Normally geometry starts with 2D, builds up angles and triangles, then much later moves to 3D.
OP, in this situation I would argue that your child saying "sometimes" shows that she could be thinking more deeply than someone who correctly said "always". They may have been thinking of a specific example (e.g the xy plane in 2D), and just leaving it at that. One should in general try to have a good proof when distinguishing whether something is sometimes true vs always true, and I don't think it is easy or trivial for a student to find such a proof for this problem early in this class. Furthermore, posing questions such as these in multiple choice format without requiring a proof/explanation, also harms students because it can hide misunderstanding such as the example I mentioned of someone assuming the right answer from one specific example, for the wrong reason. Because she picked "sometimes" I would bet she at least tried to think about the question, may have also seen easy examples like the xy plane, but she was not satisfied it can always be true, thus guessing sometimes.
Here's one satisfactory proof that it should be "always true" (assuming they've been told that 3 non-collinear points determine a unique plane, as I mentioned earlier) would go as follows: Consider the point of intersection of the 2 lines, call it A. Now pick another point B on the first line, and another point C on the second line. A unique plane passes through A, B, C by the above axiom. Thus both lines are part of this plane.
Again, I don't expect someone new to geometry to already think along those lines, but they definitely can later in the year. I honestly wouldn't worry about it, as others said. If she enjoys thinking about how and why something works, she will do fine (hopefully the class it taught in a more logical fashion going forward and hopefully she finds geometry thought provoking and beautiful).