Tuesday, January, 31, 2012
Started by having a group present parts of the calculator. Matrices.
Then talked about article (case study) that we read before class.
- How would other classes or grade levels have done/ improved with this program?
- Was there ever a time when there was some exploration of the mathematics other than in response to the errors from the pretest?
- What was the time frame that this took place in? one day, week, month? what was going on in between? homework? classwork?
- He used other software to create the quizes, so what ever the students were connected with (calculator, but might not be the TI nspire) was just to click in the answer (multiple choice).
- How would the questions have changed if it was all done on the TI nspire so the students could manipulate the figures?
- How nice that the teacher already had these questions made up.
- Is there a cheaper way?
- The teacher gave a lot of credit to the technology for the improvement of the grades of the class, but for all we know it could have been his teaching, not necessarily the technology.
- His strategy of "all being detectives" was good because it kept the smart kids engaged, and the slower kids could figure out what they did wrong. (When there was an incorrect answer the class had to figure out what was done wrong)
- He used the test bank of questions as the curriculum. The test questions are probably designed to provide as the multiple choice options the mistakes that might be made, and he used that as the curriculum.
- Question 6, a lot of people answered E, but the answer is D, which is twice the answer of E. So when students were solving, somewhere along the way they divided by 2. The teacher was surprised by this result.
- We want to give our students problems so they can "bump up against the things we want them to", we don't want it to be arbitrary, where they bump up against what ever, and that's what they learn.
- What's the mathematics here? what did students learn?
- Had a formula sheet, so they learned what the right formula is
- What i (leathem) would rather have them learn is understand the principle of being able to find the volume of a 3D figure by using area. The way you're able to do this is to take the area of the base and multiply by the height to find the area. Why does this work? layers of height of the same 2D figure (base) over and over again. Right prism.
- Underlying stuff that you find out along the way. This stuff is easy to loose or miss if it wasn't specifically being talked about.
- Just because the majority of the class got the answer right doesn't mean they actually understand the concept. If the teacher just looks at the graph and assumes that because everyone got it right then "there is no need for teaching" and doesn't talk about the problem.
- When one or two students didn't understand he talked to them privately instead of talking about the problem for the whole class.
- What could be the fault in that reasoning?: they could have guessed right, they might have it right for the wrong reason (they thought something different, or the other answers were so bogus, or that answer was the closest to what they thought might be right). They could be getting the right answer, but are way off base on the mathematics, the process just seems to work for the specific questions that are provided.
- Asking for their reasoning would help make sure everyone actually understands. Knowing why somethings wrong doesn't tell you how to do something right. But it is better than just being told you're wrong.
- But you want to spend more time on the questions that more students missed
- But there are consequences for the way he chose to set up the problem and situation, so he needs to be aware of those (using technology to have everyone send in their answers)
- Correct Misconception: not a good phrase because it means that someone has developed this idea over time, that's how they learned the material. Mistakes on the other hand are things that are done then and can be corrected then. Getting 7x8 wrong doesn't mean someone has a misconception of how to do multiplication, but that they forgot what 7x8 was at that moment. He is actually correcting mistakes (better phrase than correct misconceptions)
- Seeing student work would have helped teacher know how well students actually understood
- Is he relying too much on the technology to teach? Would it be easier for students to understand if things were written on the board, and erased....
- Technology helps teacher do more quickly what would be done on paper or whiteboard.
- How was this article received by the math ed community?
- We don't know. TI commissioned a series of case studies (including this one) and the only place it has been published is on the TI website. TI asked the teachers who are already using the technology to look at how they are using it. TI wanted people to talk about the way they are using the product. Action research. More useful for the person who does it, than for the people reading it.
- It gives us a window into the classroom where technology is being used to teach math.
- His class is made up of people who have already failed the class once before. That's one of the hardest types of people to teach because they don't think they can do the math. So to actually have a lesson plan that keeps the students engaged and interested is really powerful.
- The pretest idea with these students might be different than giving a pretest to someone who has never taken the class before.
- Name of class: Fundamentals of Mathematics
- Where did he get the calculators from? Why did he feel it was important for him to have these calcultors?
- this could be a case of the teacher saying, hum, I have this technology, but I don't know how to use it
- or a case of, hum, I can think of a great way to teach my students, now i need to get the materials (calculators)
- We will probably be in these two situations at some time during our teaching careers.