Effective teaching with graphing calculators is shown to help students develop a better understanding of mathematical concepts, use higher-level approaches to solving math problems, and score higher on performance measures.

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

• Students with graphing technology had better understanding of functions, variables, solving algebra problems in applied contexts and interpreting graphs.
• "Students' operational skills and problem-solving skills improved."

SRI International
A discussion of current research "best evidence" concluded that students who have been taught effectively with graphing calculators:

• Use graphs
• Engage in problem solving
• Are more flexible in choosing solution, making conjectures, moving among algebraic, numeric, and graphical approaches, and working with real data.

University of York
A UK review of 33 papers on ICT (including graphing calculators) in mathematics teaching found:

• Gains in understanding of particular aspects of functions.
• Pupils reached higher levels of thinking and could explain their thinking better.
• Learning gains from small group work and interaction with the teacher.

INRP
A review of 10 qualitative studies in France on the integration of graphing calculators in mathematics teaching concluded:

• Graphing calculator environments tend to promote assimilation between a function and its graphical representations to a greater degree than symbolic calculator environments.

Students' use of graphing calculators is reported to build a deeper conceptual understanding of math.

San Jose State University
In an ethnographic study of TI-89 use in a Precalculus class, the device played an important, mediating role in the progressive evolution of mathematical thought, from the concrete to the abstract, or from material to theoretical knowledge. This study provides a detailed account of how deep conceptual understanding can build through use of a graphing calculator.

Reference: (Rivera 2007)

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

• Students' operational skills and problem solving improved when graphing calculators were an integral part of instruction and testing.

Michigan State University
A review of 43 key comparative and interpretive studies found:

• The greatest benefits come from investigations which center on "what if…?" or "why?" questions.

INRP
A review of 10 quantitative and qualitative studies in France concluded:

• Students widely use calculators, even complex ones, only for simple tasks.
• Integration of the tool in a rational process of exploration, conjecture and evidence depends on the teacher to lead this integration in the classroom.

Michigan State University
A review of 43 key comparative and interpretive studies examined this issue. The review concluded:

• No significant differences in procedural skills were found between students who use handheld graphing technology and those who do not (in the areas examined).
• Extensive use of the technology does not necessarily interfere with students' acquisition of skills.

Michigan State University
A review of 43 key comparative and interpretive studies concluded:

• Students whose teachers illustrated connections between representations and emphasized concepts had greater success than did students whose teachers focused on technological and algebraic approaches.
• These teachers seemed to create classrooms with more conjecturing, multiple approaches and higher levels of discourse.
• Teachers also used technology as an extension of the way they always taught.

Michigan State University
This exploratory study focused on what students learned in algebra, how it was different for students with differential access to graphing calculators, the use of the technology on tasks of different cognitive demand, and whether the teachers' background and experience with graphing calculators might be related to student outcomes. The study considered two conditions: high quality professional development and high frequency calculator use on the part of the students, and involved three different populations: 1) teachers who seldom or never used graphing calculators in their classrooms; 2) teachers who used graphing calculators in their classrooms but without a high degree of support and ongoing professional development; and 3) teachers with a high degree of support and ongoing professional development in the use of graphing calculators for instruction. Statistically significant results (p<.004 or better) indicate that access to and use of graphing calculators seems to increase achievement, achievement decreases for both users and nonusers of calculators as the cognitive demand of the tasks increases, and while the background and experience of the teachers seems to make a difference for the top 75 percent of the students, some students perform at very low levels with or without the technology.

Reference: (Burrill and Breaux 2009) 

SRI International
While available research does not make a conclusive case, research shows that when students use graphing calculators frequently, they tend to score higher on national, state and school-level tests. Correlational studies of the relationship of frequency of graphing calculator use and achievement using:

• The National Assessment of Educational Progress (NAEP)
• Algebra I End-Of-Course Tests in Oregon and Kansas
• The Texas TAKS exam

all show higher achievement when students have access to a personal graphing calculator both in and outside of class.  An experimental study of Calculus in the Netherlands study provides the strongest evidence to date of the benefits of frequent access to graphing calculators. Research also indicates that it is not simply the frequency of access but types of use that matter.  Selective access to the calculator (depending on the learning activity) during class is a best practice.

Reference: Center for Technology in Learning (2009) “Should students have frequent access to graphing calculators? TI Research Note 3.  Menlo Park, CA: SRI International.
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Heller Research Associates
In a gain score study of handheld graphing calculator use by 458 high-school Algebra 1 students in two suburban school districts in Oregon and Kansas, using Key Curriculum Press's Discovering Algebra textbook:

• The more access students had to graphing calculators, and the more instructional time in which graphing calculators were used, the higher the test scores.
• Scores were significantly higher where teachers reported receiving professional development on how to use a graphing calculator in math instruction.

Southwest Educational Development Laboratory
In a statewide study relating graphing calculator use patterns to achievement, researchers found that:

• Students demonstrated higher levels of math performance when a graphing calculator was used.
• There was a positive correlation between the residual gain scores and students using a classroom set of graphing calculators.

Michigan State University
A review of 43 key comparative and interpretive studies examined this issue. The review concluded:

• Length of usage time affects the impact on learning.
• Quality of use counts more than quantity of use: Students whose teachers illustrated connections between representations and emphasized concepts had greater success with less time of use than did students whose teacher focused only on technological and algebraic approaches.

Virginia Commonwealth University
A peer-reviewed meta-analysis of 54 studies with the strongest form of evidence, high-quality experimental and quasi-experimental studies found inconclusive results:

• Both positive and negative effects on conceptual understanding were related to time of use.

University of Trier
A study in the Netherlands compared the performances of Calculus students in 12 classes who were randomly assigned to one of the three conditions: (1) no access to graphing calculators (control group), (2) access during one unit, and (2) access for one year. Results showed that students with year-long access to graphing calculators used a wider range of problem-solving strategies, attempted more questions, and obtained higher scores than those with less or no access. Additionally, those students who were identified as "below average" by the researchers made more frequent use of a graphical approach to problems (in contrast to a trial-and-error approach or algorithmic strategy) and scored significantly higher on the post-test.

Reference: (Harskamp, Suhre et al. 1998; Harskamp 2000)

SRI International
Three high-quality correlational studies are of particular interest:

• A study by Educational Testing Service and the College Board (Scheuneman et al., 2002) examined effects of calculator use on the SAT I math test. It concluded that “use of calculators was associated with higher test performance, but more able students were more likely to have calculators and used them more often. Overall, the effects of calculator use were found to be small, but detectable.” The effects were not influenced by gender or ability level, and were not due to simply working faster (a speeded test effect).
• A study of calculator use on the ACT math test reported that average test scores increased for virtually all groups when calculator use was permitted. This effect was found for virtually all genders, ethnicities, income levels, high school grades and courses completed (Colton, 1997).
• A study of the Tennessee Gateway assessment end-of-course test in Algebra I found that “students who responded that they used a graphing calculator performed higher than other groups” but there was no pervasive pattern across all types of calculators (Schwarz et al., 2002). There was no evidence of students failing to complete the tests (speediness)

SRI International
A review of Ellington’s meta-analysis of 54 high-quality experimental and quasi-experimental studies concluded:

• There are positive effects both for calculator use on tests and in instruction. However, one cannot separate the effects of curricular innovations made possible by calculators from a technology effect as such.
• There were no reliable negative effects in any of the groups of studies.

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.

Reference: Center for Technology in Learning, S. I. (2009). How can teachers use technology to help students with special needs improve learning in mathematics? TI Research Notes #17. Dallas, TX, Texas Instruments, Inc.

University of Iowa
A correlational analysis of the 2000 NAEP grade 8 math test data found a positive relationship to achievement, across student subgroups, for:

• Calculator access
• A de-emphasis of facts and skills, and a greater emphasis on reasoning

Purdue University
In a quasi-experiment comparing the achievement gains of 89 special education and general education students in 6th grade in two rural Michigan schools, special education students benefited as much from graphing calculator use as general education students did, though the special education students still performed less well.

Reference: (Bouck 2007)

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)

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.

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
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.

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)

Technical University of Darmstadt
In a quasi-experimental study of 6 classes in grade 7 and 7 classes in grade 9, average performance increases were above the expected increase by all participating classes. Average gains were:

• Class 7: ~12%; Class 8: ~6%; Class 9: ~10%, Class 10: ~12%

SRI International
Researchers recommend that teachers use CAS features to focus on concepts, personalize the curricular sequence to fit student needs, and emphasize meaningful mathematical tasks. Although we await evidence based upon the strongest research designs, studies throughout the world consistently report benefits when teachers integrate CAS with an emphasis on learning math concepts.

Reference: Center for Technology in Learning (2007), "Why should math teachers consider using technology with Computer Algebra Systems (CAS) features?" Research Note 10, Menlo Park, CA
Reference: Bohm, J., I. Forbes, et al. (2004). The Case for CAS. Munster, Germany, Westfalische Wilhelms-Universitat.

Zeller and Barzel 2010
In the last years, several studies have investigated the role of technology in teaching and learning mathematics. However, the specific role of computer algebra systems (CAS) in early algebra in contrast to graphic calculators (GC) is still unclear. The CAYEN project is researching this field by comparing 13-year-old pupils—one GC class and two CAS classes have been observed while acquiring elementary algebraic competences with nearly the same teaching sequence. The field of algebraic competences is split into syntactic abilities and symbol sense. The results of this explorative case study show that the development of symbol sense is influenced by the adoption of CAS in the learning process. Especially when transitioning from arithmetic to algebra, the pupils’ views of algebra as well as their conceptions of algebraic objects seem to be affected by the availability of CAS.

United States Military Academy at West Point
An experimental study on CAS in a core calculus course found:

• The experimental group attained a higher mean score than the control group on 13 of 20 items.
• Among the 20 items, the only significant differences in mean scores (p < 0.05)="" were="" found="" in="" eight="" of="" the="" items="" favoring="" the="" experimental="">

University of Wuerzburg
A multi-year study is under way of the use of symbolic CAS calculators  – the TI-Voyage 200 – in six 10th grade classes of three schools in Bavaria (Germany).  The main results of the first two years of this project are (see Weigand 2008):
• The students improved their competence in areas in which a symbolic calculator can be beneficial: working with graphs of functions and switching between representations. 
• No difference was detected when working with variables, terms and tables. This shows in particular that development of algebra skills was not hindered with the Symbolic Calculators in classes.
• There was an improved performance particularly amongst the poor and average groups, whilst the “good” students improved only slightly. 
• The mathematical beliefs and attitudes of the students with regard to new tools are mixed.
• It is not clear how sensitive the class tests were to the learning outcomes expected from symbolic calculators use. 
The teachers’ lesson reports confirmed that the calculator is a catalyst for “new” teaching methods.  Individual work, as well as partner and group work in mathematics lessons, appeared to be reinforced.

Reference: (Weigand 2008)

City University of New York
In a descriptive case study, data collected from surveys and reflection journals for both secondary and elementary education groups show that pre-service teachers' perspectives strongly depended on the intensity and length of experience they had with the use of technology. More experience and practice provides pre-service teachers with a better understanding of the benefits of technology for their future students as well as for their own learning. However, the effect of integrating graphing calculator technology into methods classes on the pre-service teachers' confidence in the use of this technology was different for secondary and elementary education participants.

Reference: (Lyublinskaya, Donoghue et al. 2007)

Brooklyn College-CUNY
A small-scale descriptive pilot study of pre-service teachers using TI-Nspire found the crucial, perhaps, decisive effect that modeling of exemplary practice in the field placement has on candidate attitudes regarding the use of advanced digital technologies in their teaching

Reference: (Meagher, Ozgun-Koca et al. 2008)

Florida State University
A case study introducing TI-Nspire to 35 pre-service math teachers in 2 cohorts found that:

• the new technology served as a tool or stimulator in fostering pedagogical reflection among the participants.
• the new technology stimulated among the participants a willingness to learn on their own and with their students.
• participants' beliefs and prior experience played an important role in their justification of their proposed ways of teaching and assessment.
• participants experienced tension between traditional curricular materials (e.g., the textbook) and the need to recreate their instructional tasks.
• the new technology can at times lead to conflicts between participants' traditional view of mathematics teaching and their awareness of innovative alternatives.

University of Massachusetts - Dartmouth
In high quality experimental studies, SimCalc has shown strong effects for teaching mathematics in a technology-facilitated environment. At the heart of the model is the use of technology to integrate graphical, dynamic and linguistic representation to enhance student learning. At Texas Instruments, we see implications that extend far beyond the project and are important to the entire graphing calculator and classroom networking community in math and science education.

Reference: (Hegedus 2007)

Indiana University Purdue University Indianapolis

Brigham Young University

3 key factors impact teaching and learning of mathematics with GC: access to GC, the place of GC in the mathematics curriculum, and connection between GC and pedagogical practice.  Implications  for preservice and in-service teacher ed are summarized.

Reference:  (Kastberg and Leatham 2005)