# Teaching and Learning with Graphing Calculators

## Attitudes Towards Math

**Conclusion:**Effective use of graphing calculators has been shown to improve students' attitudes toward math.

**Virginia Commonwealth University / SRI International**

A peer-reviewed meta-analysis of 54 of studies with the strongest form of evidence, high-quality experimental and quasi-experimental studies concluded:

- Students using graphing calculators in instruction had significantly better attitudes toward math than those not using the technology in instruction (effect size .49 across 8 studies)

*(Ellington 2003)*

Reference: Center for Technology in Learning (2007), "How can teachers translate students' positive attitudes towards ICTs into better mathematics learning?" Research Note #12, Menlo Park, CA

**Conclusion:**Skilled middle school mathematics teachers who use calculators can positively affect students' attitude, confidence, engagement and achievement.

**Northern Arizona University**

A review of middle school peer-reviewed studies using qualitative and quantitative methods concluded that when technology (including calculators) is used well:

- Positive effects can occur on students' attitudes toward learning, confidence in their abilities to do mathematics, engagement with the subject matter, and mathematical achievement and conceptual understanding.
- The effect depends on the teacher's skill in integrating technology into the curriculum.

*(Guerrero, Walker et al. 2004)*

**Conclusion:**Addressing students’ special needs must start with getting the foundations of mathematics teaching right. Within good teaching practice, technology can support special needs students by offering multiple ways to represent mathematics, support action and expression, and engage students’ interest, consonant with the principles of Universal Design for Learning.

**SRI International**Overall, the trend in research with special needs and ELL students is for teachers to avoid taking only one specific, narrow approach, but rather to acquire skills in differentiating instruction so that alternative approaches are routinely used to better meet the learning needs of all of their students.

To respond to students’ difficulties in processing information and distinguishing relevant information, teachers may engage additional modes of representation and expression made available through technology. To address students’ low esteem in response to their difficulties in traditional classroom formats, teachers may use technology to give students new modes of expression and new means of engagement.

To help students move on to higher order mathematics reasoning, without getting bogged down in mechanical computations or procedures, some of the cognitive load may be offloaded to technological capabilities to compute and visualize. Students who are reluctant or passive learners may become more active when exploratory or collaborative modes of engagement are available as part of the classroom repertoire.

Overall, self-regulation is strongly encouraged in a more interactive mathematics classroom, because students have more opportunities to try mathematical actions and see the resulting mathematical consequences, as well as the potential for more support from their peers through social and collaborative activities.

*(SRI International 2009)*

**Conclusion:**To improve mathematics in low-performing schools, educators should address a broad range of factors systemically, including an intensification strategy, coherent curriculum, effective pedagogy, deeper teacher mathematics knowledge, positive social factors and supportive organizational structures.

**SRI International**

This note summarizes a research-based Conceptual Framework developed to help educators and researchers comprehensively understand the factors involved in improving mathematics instruction. They can then make better choices about which intervention to pick, or how to supplement or customize a chosen intervention for their local setting.

To develop the conceptual framework, a team of researchers examined two research literatures: the cognitive sciences research literature on how people learn and think about mathematics, and the international comparison literature examining approaches to teaching and learning mathematics in different countries. In addition, the framework was informed by a review of 17 interventions in mathematics. Reference: Center for Technology in Learning, S. I. (2009). A comprehensive framework for improving mathematics in low-performing secondary schools. TI Research Notes #16. Dallas, TX, Texas Instruments.

**Conclusion:**Using the graphing calculator helped students maintain productive affect for problem solving.

**McCulloch 2011**

A qualitative study of six high school calculus students designed to build an understanding about the affect associated with graphing calculator use in independent situations. framework for affect as a representational system was used as a lens through which to understand the ways in which graphing calculator use impacted students’ affective pathways. It was found that using the graphing calculator helped students maintain productive affective pathways for problem solving as long as they were using graphing calculator capabilities for which they had gone through a process of instrumental genesis with respect to the mathematical task they were working on. Furthermore, graphing calculator use and the affect that is associated with its use may be influenced by the perceived values of others, including parents and teachers (past, present and future).(McCulloch 2011)