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Case Summary

A high school teacher uses a graphing calculator to teach a precalculus class.

Setting the Scene

  • Applicable Grade Level(s): grade 9;grade 10;grade 11;grade 12;
  • Applicable Subject/Unit(s): Math;
  • Technologies Used in Lesson: graphic calculator;spreadsheets;other;
  • Kind of School: high school (9-12 or 10-12);
  • School Location: suburban(major city);
  • Connectivity: link to world (WWW);
  • Location of Technology Resources: most located in classrooms in adequate numbers (more than 1-2);
  • Social Economical Situation of Student: mixed middle class and affluent;

Teacher Information

  • Teaching Experience: 30 years
  • Teacher Technology Experience/Skill Level: used consistently at home and in classroom;

Other Case Details

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Whole Story



So you use graphing calculators with your students on a daily basis?

Every day.

Tell me how that works. Why are you using them?

Why are we using the graphic calculators? Well, you cannot survive in any type of job activity now, without having some type of calculator or computer background. Itís hard for them to carry a computer around, but they can do a graphing calculator. And on that, we can do statistical analysis, we can do spread sheets. So they are hands-on activities. We each have a classroom set of 25 that we keep in our room, in case the students forget theirs. Or, if they cannot afford them, weíll furnish them for the student. Basically, this year, they need to buy their own calculator.

Oh.

And so, the advanced placement exams are the ones that really helped facilitate bringing the graphing calculator into our school system, since they need them to be successful on those exams. We basically are saying then, that all students will need them to be successful in getting to college and surviving college. So, basically, from geometry up, graphing calculators are used almost daily. Not only that but theyíre also used in our integrated classes, that start with freshmen... Well, they really start with seventh grade, where the Texas Instruments 83 + is used almost daily.

OK. Tell me about one of these activities, like you mentioned using the spreadsheet. And tell me about it in terms of what is your learning outcome? Do you have them do a spreadsheet assignment?

OK, an activity that weíre going to be doing next week, we have a slinky that is suspended from a yard stick across the back of the chairs. And on the bottom of the slinky is a film canister connected with a paper clip and then what we do is we measure the distance the film canister is from the floor. Then what happens is, we put in three M&Mís and we measure the distance. Then we put in three more M&Mís and measure the distance. Then we put in three more M&Mís and measure the distance so it can hold up to 30 M&Mís. And then from that, we put that into our lists. Our list one is the number of M&Mís we put in the container. List two is the distance from the floor. And from that we do a linear regression line. Now these are my Algebra IB students, who are basically freshmen students that are struggling with mathematics, or do not have any, or have great math anxiety. This shows them... This is a basic-level activity.

Great. I want to ask you, what is the studentsí demeanor during this activity? Are they engaged?

Yeah. Anytime you can get the students engaged in an activity in class, itís much more meaningful for them, but also they retain it a lot longer. You can just say, "Remember the M&M activity?" and they are going to say, "Oh, yeah." And I use M&Mís that are like 30 years old. No, they are not quite that old, but maybe 10. So they know they are just covered with germs and dirt, so they do not eat the M&Mís, and then I treat them by giving a spoonful of M&Ms. And M&MS are so uniform, so they are wonderful objects to do activities with.

Do you think there is a difference between doing it with the graphing calculator as opposed to doing this activity without...

Well, we have to do it on paper and pencil first.

Oh, OK.

They have to do all of their graphs. Everything with paper and pencil so they know exactly what they are. And we also write up the equation for the line by hand, so they have their own best fit line. Then we put it in the graphing calculator, and then the oohs and aahs start.

Why do the oohs and aahs start when they do that?

Well, because they are just saying, "Why didnít we do this before? This is so fun, and I see why everybody wants to have a calculator." We can do things so much quicker, and you know, they can instantly see the results. But then I also stress to them that there are certain limitations to the calculator that it cannot do. But we can do these because we are so much smarter than the calculator.

OK.

And also itís a double check to see if their linear regression line is going the right direction and so forth and so on.

Do you ever have difficulties with students using the graphing calculator? I mean, Iím sure there are some students that maybe have a difficult time doing that, and how do you scaffold the activity for them?

What you do is, I have an overhead projector, and I have a student in control of that. So that student sets the pace of the room.

OK.

And then, as Iím giving the student instructions on what to put in, Iím walking around the room and trying to handle the questions as they go up. And we do not go on until everybody sees a certain window. To start with, like today in advanced algebra, I just said, "How can you put a polynomial equation into the graphing calculator? Do you know how to find the x-intercepts? Do you know how to find the y-intercepts? Do you know how to find the relative means and maximums?" And if they say, "Yes, yes, yes," then we move on. And if they donít, we stop and demonstrate. But if everybody knows how to do something, then we just quickly move on. So we can approach the problems and go into a lot more depth by using the graphing calculators in the classroom.

How do you assess their learning?

We assess their learning many different ways. One is they need to show me what they have in their graphing calculator as a lower level. They need to show me what they have. And if they show me what they have, I have a checklist they can go back and do some more work.

So you kind of do an observational assessment?

Right. I walk around with a clipboard, making sure they have certain things before they can go on. In the upper-level classes, we have examinations that are assessed differently. We have examinations that they have to do without using the graphing calculator and we have examinations or questions on the exam that they have to do with the graphing calculators and come up with the answers. So itís all right, or itís all wrong. We also have questions on our assessment tools that make the student think about whatís happening. "Here is a graph. From this graph, what can we tell?" And so we try to do both. Well, the teaching part is twice as much teaching now as we ever did. So you have to teach everything without technology and how to do things with technology because it depends upon what university they are going to go into, what classes they are going to go into, or what field they are going to go into. They are going to need to be able to do both.

It sounds as if you are doing some formative assessment and then the summative assessment with the exam.

Right. And also with their homework.

Right. You use this graphing calculator all year long?

Right.

OK. How long are the class periods where you are using it?

Well, that depends upon what schedule weíre on.

OK.

We have eight different schedules but basically 43 minutes.

And youíve implied this really well, but Iím just going to ask you to restate what your role is as the teacher as the students are using the graphing calculators.

More of a facilitator. The students are in charge of the teacher overhead in front, and the students have their own graphing calculator, so I just walk around and ask questions.

Great.

And answer questions.

If a teacher were going to try and implement using graphing calculators in their classroom, what is some advice that you would give them?

You are not Gods. You learn from your students. And thatís one of the things that you have to be able to do nowadays as a teacher. You wonít know all the answers instantly. And you have to be able to tell your students, "Iím not sure but Iíll find out and weíll regroup." And, I would say that if you are going to be using the graphing calculator, you need to go through some training. You can pick up a lot by reading the book, but you can pick up so much more by going to a class and learning from your peers. And I know that Texas Instruments has wonderful courses in the summertime that are one to two-weeks long. They are set up for algebra I, geometry, algebra II, precalculus, trig... They have them for chemistry. They have them for physics. Also, I think that teachers need to be professional and attend their math conferences or their science conferences, and from there, you will find a lot of sessions on technology. The National Council of Teachers of Mathematics, which will now be having theirs in San Antonio, will have probably 100 sessions on technology that you can go to. Plus night workshops that you can go to. So, donít isolate yourself. And donít believe that you cannot teach something unless you know it all.

Great. The last question: are these activities associated with standards for...

Oh, yes. Yes. Our standard books are well used. As a matter of fact, I think I am on my third of the new editions. Our benchmarks and the framework of our school is set up according to the standards. Now we are in the process of reanalyzing the standards and reemphasizing them because of the No Child Left Behind Act. Because we have to be able to assess every benchmark that we have. So rather than having 4,000 benchmarks, now weíre doing groups of benchmarks and having questions to make sure that they have made those benchmarks.

Excellent. Iím not going to take up any more of your time.

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