Plug-and-chug. That’s one way in which Anna Cox, instructor of mathematics at Kellog Community College (Battle Creek, MI), describes how she once went about assessing student progress. Other terms that came to mind: rote memorization and number crunching. One year ago, Cox got her hands on dynamic TI-Nspire CAS technology and realized that she needed to chuck her plug-and-chug questioning when it came to in-class activities and tests.
“(With TI-Nspire CAS technology), I’m able to ask many more conceptual questions where my students have to explain what’s happening and why it’s happening versus giving them 20 plug-and-chug kinds of questions,” she said. “Teaching has to change because we have tools that will do the number crunching for us. We have to now start thinking about different ways to make meaningful teaching and learning occur and that’s what I’ve trying to do using TI-Nspire CAS.”
Understanding beyond the textbook
Realizing that TI-Nspire CAS functions allow for a deep, interactive exploration of mathematical concepts, Cox is asking more open-ended questions of her students. It’s a way to challenge her students to further explain their answers rather than simply stop at numeric or symbolic outcomes reached on the handheld. They are expected to make connections based on critical thinking and take into account observations and patterns they discover while using TI-Nspire CAS technology’s interactive capabilities. One example of this is how Cox transitions her class from a section on factoring to a section on graphing.
“My students need to understand that the factors of an equation are really just the x-intercepts and I have found that many textbooks do not make this connection,” she said. “One of my test questions may be: ‘If two-thirds and ½ are the x-intercepts, how does this relate to the equation of the graph?’ Students must have comprehension.”
It helps that Cox and her students can use TI-Nspire CAS technology to split the screen in order to view multiple representations simultaneously – for example, a factored equation on one side and graphed function on the other. Both are linked together. In other words, as the equation’s variables are changed, the graphed function changes instantly. Students can make immediate conclusions based on different inputs. This ability to manipulate representations in real time, on the same screen, is a feature unique to the TI-Nspire CAS handheld and computer software.
“It’s not just that they are taking an equation and graphing it, or taking an equation and factoring it,” Cox said. “Instead of showing me you can do it, you have to describe what you are doing. That eliminates the response of: ‘Well, here’s my answer I got on the calculator.’ As a teacher, I want to know the steps students take to get an answer.”
Driven to problem solve
Cox emphasizes the goal of problem solving to her students, exploring the “how” and “why” toward developing greater conceptual understanding. It’s an instructional approach well supported by the dynamic capabilities of TI-Nspire CAS technology, although yet to be fully embraced by fellow math department faculty members, according to Cox.
“I didn’t use conceptual questioning in the beginning and I think that is where the rest of the faculty is right now,” Cox said. “I think they believe it ought to be done but they are not doing it for different reasons. I think they believe what they are doing is working; however, I’m not convinced that students understand what they are doing.”
Cox added: “When my students say they are never going to use this kind of mathematics in their future jobs, I tell them that maybe they are right but they are going to understand how things are related to each other. I emphasize frequently that we are about problem solving. Can you understand, given any situation, how to think it through to a logical end? The types of questions I ask have drastically changed.”
No right answers, just many perspectives
During a regression activity to determine medicine dosages for children, Cox uses TI-Nspire CAS technology to encourage her students to compare plotted points on a graph to decide how much medicine is appropriate or needed.
“TI-Nspire CAS helps make it easier to do regressions and I use this capability to provide students two formulas that relate to how people and pharmacies figure out medicine dosages for children,” Cox said. “Is it better to use the formulas that give the higher dosage or the lower dosage and why? We find at what point the two dosages are the same and at what age. We have these two formulas for graphing and plotting, which helps student see the ages for the highest and lowest dosages. We can get a good discussion going.”
Since the community college classroom represents a rather diverse demographic of traditional and nontraditional students – a range of age groups – the choice to give a child either more or less medicine extends beyond the plotted points on a graph, according to Cox.
“There’s no right or wrong answer,” Cox said. “Students just need to justify their viewpoints. I am amazed at what students can do if given the right tools and right encouragement. The things they come up with are amazing.”
Cox began using a class set of 30 TI-Nspire CAS handhelds during class in the spring 2008 semester. She has continued to incorporate them into her instruction for summer and fall courses.
“I use the TI-Nspire CAS Computer Software – Teacher Edition daily and students have their handhelds,” Cox said. “I like being able to do things on the software quickly and then walk around the classroom to help my students.”
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