At the end of year as we were preparing for the EOC, our department faced a dilemma: we didn’t have enough calculators to provide to every student in a math class. This brought up the discussion we had had since we adjusted our curriculum guide from a lesson-by-lesson, section-by-section, pacing to a concept-by-concept pacing:
- When are calculators an acceptable teaching and learning aid, and
- how do we avoid students using them as a crutch?
We are asked to integrate technology in the classroom; we hear suggestions to take the importance of calculation out of the learning and focus on the conceptual understanding; yet we use blurry focus to see the fine line between using the technology for learning mathematics and creating dependent students.
I want to broaden my understanding and expand my methods for using calculators in the classroom. I want to minimize calculator dependency and maximize conceptual learning. If students are expected to provide evidence of learning on a high-stakes test, then we claim that they should be able to perform well in the “basics” and be proficient in the subject. If we forget teaching the basics with calculators and claim that students should be able to pencil-and-paper calculate the sum of two mixed numbers, or graph the square root function, then to where else should we cut calculator use and demand nontech calculation? We run into problems when a test is written to be taken using either a calculator or not, yet some of the problems can be accomplished quickly by those who know how to effectively use a calculator.
We need to explore ways students can effectively learn mathematics using a calculator,we need to define the areas where calculators can detract from the learning, and we must carefully define how a calculator can benefit students without supplanting the goal of learning mathematics. If we see successful scores and intelligent conversation about a math concept, then we need to define the role calculator use has in that situation.
Where does calculator use enhance or detract from the learning?
Calculators are tools to make things to learn a concept , so we can use the calculator, but if we have not calculator, we can looking for another tool.
Where? where it needs.
After at least 20 years of studying this issue I have changed my mind. I use to think and teach that it was all about making sure that the technology is not short circuiting the students math thinking. In other words, decide what you type of thinking you are teaching and make sure the technology (calculator) is being used appropriately. The problem with this pedagogical view is student want to do the least amount of thinking possible. The teacher can say, do not use your calculator on this problem, but unless it is a controlled exam; the teacher doesn’t have control of how the students use calculators.
My present view is choose math activities with high rigor and monitor how students are using technology. Use your observations to make adjustments to how you write assessments, choose activities, and ask questions to keep the students thinking.
A couple of examples, here is an education article published by TI but it is really about increasing math rigor and very little about how important calculators are to learning math http://education.ti.com/educationportal/sites/US/nonProductMulti/communitycollege_feature_article.html?bid=5
Another example, is the importance of finding both exact answers and decimal approximations. As a teacher how is best to motivate correct use of calculators and see the need to exact answers rather than police the students about calculators.
I found though that as I taught a calculator exploration, I had to teach students how to use the calculator and my lesson became less of a mathematics lesson and more of a tutorial on the calculator.
I highly value the use of a calculator in the classroom, and without trying to be contrary to my post, and according to research I’ve seen, calculators can have high impact in student learning depending on the activities present, but I want to ensure that my students are maximizing their ability (for their level) at using the calculators. I wonder if TI has some sort of “pretest” to hand out to determine what students can actually do with the calculator.
Gracias for this calculators