Summary:
Article:
We read the article "Improving Student Performance with the TI-Navigator System: A Pedagogical Journey" by Derrick Driscoll. Mr. Driscoll is a math teacher, and this article is a case study about a new strategy he used to teach students math. The class that Mr. Driscoll experimented on was a ninth grade class of students who had already taken the class before but hadn't passed. The class was called Fundamentals of Mathematics. The article describes the process Mr. Driscoll used. He started by giving the students a pretest. The subject they were learning about was volumes of prisms, so that was the body of the test. From the examples shown it looked like the whole test was multiple choice. The students didn't have any prior instruction about the topic, but they did get to use a formula sheet. Mr. Driscoll collected the data (scores) from the students on the TI navigator system so he could then look at class averages over all and for individual problems. He took the scores that he got and decided to review the problems that were missed most frequently. The ones that most of the class got right he decided to skip. He called this going over problems "Correcting Misconceptions". After going over the mistakes as a class, Mr. Driscoll went onto his next step, "Assess and Consolidate". He again gave the students a test, a post- test, to see what they had learned from reviewing the pretest. Using technology, like for the pretest, he was able to look at the new scores, class averages, question averages, and individual performance. He said he answered two questions with the post- test: 1) Did the class average increase due to increases in student performance on triangular prisms? 2) Did the class continue to perform as well on the balance of the prism styles even though they were not discussed in the lesson? He answered yes to both questions. Mr. Driscoll includes near the end of his case study a lot of information (tables, lists, graphs) about different subjects that he taught, average scores that people got on pre, post, formal, and other tests that students were given, and he provides this data for a few semesters. From his research/ case study Mr. Driscoll draws the conclusion that using the technology in the manner that he did has a positive effect on learning in comparison to traditional methods. Mr. Driscoll says that having technology that provided him with on the spot data (student scores, who was correct, who was not) helps him see where his students are struggling right away. He says, "there is no blaming and there are no excuses. We are all detectives."
Class Discussion:
Our class discussion started with a few questions: "How would other classes or grade levels have done with this program?", "Was there ever a time when there was some exploration or the mathematics other than in response to the errors?", "What was the time frame that this took place in? one day, week, month? what was going on in between? homework? classwork?", "How would the questions have changed if it was all done on the TI nspire so the students could manipulate the figures?", "Is there a cheaper way?". Then it was mentioned that 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). We thought it was interesting that he used the test bank of questions as the curriculum, and realized that the test questions are probably designed to provide as the multiple choice options the mistakes that might be made, and he knew those mistakes would be made, so he could use it as the curriculum. Dr. Leatham pointed out that 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. The stuff they might bump up against can be 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. Our discussion then turned to Mr. Driscoll's choice to not review questions where most of the class got the answer correct. Someone pointed out that 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 then he could be missing some mistakes that people made that still lead them to the correct answer. Although he did say that when one or two students didn't understand he talked to them privately instead of talking about the problem for the whole class. Someone in our class thought that 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. We then talked about his choice of words when he said "Correct Misconceptions". That's 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, which is a better phrase than correct misconceptions. We were impressed though that his class is made up of people who have already failed the class once before, and that's one of the hardest types of people to teach because they don't think they can do the math. So this method he used which actually was a lesson plan that keeps the students engaged and interested is really powerful. Our class discussion concluded with the question "Where did he get the calculators from? Why did he feel it was important for him to have these calculators?" Mr. Leatham pointed out that there could be two different reasons for having the calculators and doing this case study. First, this could be a case of the teacher saying, "hum, I have this technology, but I don't know how to use it", so the teacher found a way to use it. Or second, "hum, I can think of a great way to teach my students, now i need to get the materials (calculators)". We, as teachers, will probably be in these two situations at some time during our teaching careers. If we want something we need to ask for it, and if it is for a good purpose we will probably be able to get it.
Critique:
I was impressed by Mr. Driscoll's method of teaching because he was able to improve test scores of students who he knew struggled with the concepts. That is something that I hope to be able to do (improve grades of students who are obviously struggling) because I'm sure that I will have students in my classes who struggle, but I still want them to learn and love math the way I do. I wasn't sure that the technology that he used was necessary. What I mean by that is it seems like he used expensive technology for a really simple purpose, I think it would have been more advantageous to buy cheaper materials, unless the teacher plans on using all of the functions of the technology, not just the information gathering part.
Connections:
My connections are actually very similar to my critique. I believe that all student deserve the opportunity to learn and love math. Mr. Driscoll understood that these students had already been taught the material through traditional methods, so he needed to find a different way to teach these concepts to the students. That is a very important lesson for me to learn. Not all student learn the same. Even students who excel in my classes. I needed to remember that there isn't just one way to teach, and in fact, if I do a little bit of research I can probably find more was that I had not thought of before.