But if it is the question, you need an answer that reflects putting students’ success at the forefront. I have been asked this question all too often recently by both administrators and educators at all levels. Of course, the technology they are usually referring to is the calculator. With the release of the Calculator Policy statements by PARCC and SBAC as well as state assessments such as the TN Ready in my state of Tennessee, many teachers, principals, and district level personnel have often made the decision to eliminate calculator use from the classroom. “If they can’t use it on the test why should we let them use it in the classroom?” That is the rationale for many of the decisions that have been made.
As with any educational strategy or tool, in this case – technology, more specifically calculators or
handhelds – the implementation has to be effective. Effective technology integration supports curricular goals. To effect change with the learner, the use of technology must employ the active engagement of the learner through participation alone as well as in cooperative groups. Frequent interaction and feedback from the teacher, as well as peers that moves the learning and the learner forward, is also needed. The teacher becomes the conductor as he/she orchestrates rich mathematical discourse around the investigation.
Students need to “use appropriate tools strategically” (CCSSM.SMP.5). They need to understand what the calculator does for them, what it does not do for them, and when and how it can help them develop a deeper understanding of the mathematical concepts they are investigating. And this is true from the elementary grades through the secondary course. Take a look at two examples: one from the elementary strand and one from the secondary strand.
The TI-15 is a powerful, pedagogically correct tool of investigation. This tool, when coupled with a rich activity such as “100 or Bust” from Texas Instruments, supports the development of deeper understandings of the foundational concepts of place value. Effective facilitation of this task includes reading a trade book, thus providing a literacy connection as well as guiding mathematical discourse through effective questioning. Students develop an appreciation for each of the three types of “tools of investigation” that are employed. And the activity can be easily adapted for use in kindergarten to the middle grades.
Being able to communicate important foundational mathematical concepts, employ multiple representations, and move from the concrete to the symbolic and abstract is vital for making mathematics accessible to all learners. Young mathematicians experience patterns and make conjectures based upon those patterns as they work with investigations that can be scaffolded to support their individual needs using their “tools of investigation.” Using these tools, they move beyond just knowing a rule to truly understanding the why. So “calculators not used in the test” is not the point at all. Calculators are used to foster learning, discovery, and memory.
Secondary students are now encountering mathematics that for many can be quite challenging, especially when they may have gaps in their mathematical experiences. Walk This Way (Texas & Jones, Strategies for Common Core Mathematics: Implementing the SMPs, Eye On Education, Routledge) is an activity that allows participants to use repeated reasoning to investigate mathematical concepts in a variety of graphing situations by physically representing mathematics on a life-size graph first. A variety of mathematical topics can be modeled – integers, basic linear and quadratic functions, complex numbers, and polar graphs – to cover the secondary bands. Investigating graphing kinesthetically at any level supports the development of deeper understanding and increased retention.
Students physically analyze how various graphs are transformed both on a number line and a variety of coordinate grids. By asking probing questions rather than just repeating formulas and telling how each of the components of an equation affects the graph, students are better able to develop meaning on their own and understand how functions behave. Students are able to understand and convey why certain changes to equations transform a graph as they work both on table top grids & number lines, floor grids and number lines, and on a graphing calculator/handheld. Technology is employed both as a tool of investigation and as a way to check and to make connections to other representations of equations and functions. Literature, again, can be utilized to support developing mathematical concepts. Extending these basic concepts students can engage with the TI-Nspire iPad APP and create graphs to model real-life contexts, such as this art exhibit found in an airport. Students again are engaging kinesthetically by “touching their math” on their iPad! This is truly a powerful experience for students to have.
So do we use technology or not? Technology, used in collaboration with rich tasks, other tools such as manipulatives, literature, etc., effective facilitation, and meaningful discourse can level the playing field for students by supporting making mathematics accessible to all learners, no matter what their grade or level. So what if calculators cannot be used on all the test? The true power of the calculator or handheld comes into play as it is used as a tool of investigation – not just a number cruncher. Teachers can and should frame assessment experiences that model the next generation of assessments their students will be taking. But in preparation for those assessments and in preparation for the next mathematical experiences students will encounter on their mathematical journey, the calculator/handheld is a powerful tool that all students should have available in their mathematics toolkit.