In Bavarian Grade 10 math classes using CAS:

-Competence improved in topics involving work with graphs and switching between representations.
-Algebra skills developed developed to the same level as non-CAS classes.
- Poor and average students improved more than good students.
- Student reaction to the graphing calculator was mixed.

In addition, teachers reported that new teaching methods are possible with the technology, in individual, small and large group work.

There is direct correlation between quality and frequency of use of TI-Nspire in the classroom and teachers’ and students’
attitudes and proficiency.

By using the handheld, the students made the connections much quicker and seemed to understand the concept of how equations relate to lines and how they relate to the slope and vertical intercept.

I think that many students were able to make a visual connection with the graphing and the action that created the graph.

Dr. Lapp gives an example of how he posed a problem to his students and they used multiple representations to solve the problem, building their own deeper understanding of the behavior of functions.

Using TI-Nspire, at midyear Ms. Hoyt had 2 to 4 times as many students in the “Basic” or “Proficient” level, compared to other teachers’ classes not using TI-Nspire

For the most part, the experiment could not discern an impact as a result of providing the equipment and training for TI-Navigator. As shown in the figure below, we found a modest effect for Geometry achievement using the NWEA End of Course Geometry test. This figure shows the outcome measure in standardized units. However, this impact was not reflected in CST Geometry scores. In Algebra, while we found no overall difference, there was some evidence of a small negative impact for students scoring “below basic” on the CST and, holding pretest score constant, for English proficient students. The results of the NWEA End of Course Algebra I test did not reflect those same results. Implementation must be considered in interpreting these findings. Our surveys and observations make clear that this implementation was not a fair test of the difference TI-Navigator might make if used more extensively. Of the 19 teachers originally assigned to the treatment group, about half did not use the system at all for instruction. Of the remaining nine teachers, only three could be considered “Comprehensive-Implementers.” Of those three, only one used TI-Navigator daily. Technical glitches deterred many from using the system after previous failed attempts. Overall use may have been constrained by the fact that California prohibits calculator use on state tests. Impact on NWEA Geometry Achievement Our results also must be qualified by the fact that, while finding differences on one test, we did not find differences on the other test. The  significant amount of attrition, both at the teacher and student levels, although not believed to be associated with the program being tested, raises issues about generalizability. For example, it is clear that in both experimental conditions, lower scoring students were significantly more likely to not have posttests, indicating that our findings are not applicable to the lowest scoring students in these districts. Overall, we found that the TI-Navigator affected the average number of minutes the technology was used. The teachers with TI-Navigator reported using the technology about 15 minutes more per week per class period than teachers without. Future exploratory analyses may prove useful in suggesting whether extent of usage can account for student outcomes. In particular, since TINavigator resulted in greater technology use, examining the correlation between technology use and achievement may suggest a mechanism by which TI- Navigator could be effective. Future studies of TI-Navigator will benefit from greater support for implementation. We also recommend continuing to include Geometry in the topics to which TI-Navigator is applied, since the positive result found in this experiment should be replicated.

This study investigated the relationship between instructional use of handheld graphing calculators and student achievement in Algebra 1. Three end-of-course test forms were administered (without calculators) using matrix sampling to 458 high-school students in two suburban school districts in Oregon and Kansas. Questions on two forms were drawn from Texas and Massachusetts publicly released standardized test items, and the third form was custom-designed to emphasize conceptual understanding and math applications. All classes used Key Curriculum Press’s Discovering Algebra textbook. Results showed that the more access students had to graphing calculators, and the more instructional time in which graphing calculators were used, the higher the test scores. In addition, scores were significantly higher where teachers reported receiving professional development on how to use a graphing calculator in math instruction.

The data represent a reduced achievement gap between Integrated Algebra and College Prep Algebra. In Year 1, the gap declined from a 14.02% difference to a 8.18% difference in average number of proficient students. In Year 2, the gap declined from a 14.91% difference to 7.54% difference in the average number of proficient students.

This paper reports preliminary analyses comparing results on the state-administered 8th Grade and 9th Grade algebra Texas Assessment of Knowledge and Skills (TAKS) for a treatment and a control group. The treatment group consisted of 127 students from algebra classes at a highly diverse school in central Texas taught by two relatively new teachers using a network-supported function-based algebra (NFBA) approach as integrated with the ongoing use of an existing school-wide algebra curriculum. The control group was comprised of 99 students taught by two more-senior teachers in the same school using only the school-wide algebra curriculum. The intervention consisted of implementing 20-25 class days worth of NFBA materials over an eleven-week period in the spring of 2005. Because the students were not randomly assigned to the classes, the study is a quasi-experimental design. Using a two sample paired t-Test for means, statistically significant results for the treatment group (p-value one tail = 0.000335  > alpha = 0.05) were obtained.  We can conclude the NFBA intervention was effective in improving outcomes related to learning the algebra objectives assessed on the 9th Grade TAKS.

This paper details the motivation, background, and analysis for studying the effect that an Increasing Achievement on Algebra Assessment (IAAA) workshop for a group of Florida high school teachers had on student pe/jormance in statewide testing. The main focus ofthe workshop was to provide participating teachers with both instruction and activities related to problem-solving techniques using the TI-83 Plus handheld graphing calculator that the teachers could then use in an effort to better prepare their students for state-wide testing. Overall, students (n = 328) who were taught by IAAA-trained teachers between consecutive annual statewide assessments had a greater gain in test scores than students (n = 202) who were taught by non-trained teachers. In particular, the data indicates a significant increase in scores for students taught by IAAA-trained teachers in a general mathematics course, as compared to no significant increase in scores for students taking that same course taught by non-trained teachers.

New Jersey’s urban students traditionally don’t do well on the high stakes NJ High School Proficiency Assessment. Most current remedial mathematics curricula provide students with a plethora of problems like those traditionally found on the state test. This approach is not working. Finding better ways to teach our urban students may help close this achievement gap. This study examined whether a problem/project-based data analysis unit incorporating the document features of the TI-Nspire would help students master data analysis concepts. The study used a quasi-experimental pre/Post-test design enhanced by a qualitative component. A four-week problem/project based data analysis unit served as the curriculum for the intervention treatment. Students were assigned either the TI-84 or the TI-Nspire calculator. Twelve sections of ninth grade students were divided into four basic study groups: (Intervention (TI-84), Traditional (TI-84), Intervention (TI-Nspire), and Traditional (TI-Nspire)).
The quantitative component of the study analyzed differences between students’ pre/post- Total, Multiple-choice, Open-ended mean scores and quantified attitudinal responses. The analysis showed students in the TI-Nspire groups improved more on the Total test and Multiple-choice questions while students in the TI-84 group performed better on Open-ended questions. The Intervention Curriculum was more effective for Multiple-choice questions, Traditional Curriculum for Open-ended questions and Total scores. Student interviews revealed they didn’t like taking notes and answering questions on the TI-Nspire. Some students liked referring to the information in the calculator while others felt that accessing information was too time consuming. The merits of the TI-Nspire document feature needs further exploration. Analysis of the quantified attitudinal survey showed an increase in the positive attitudes of students using the TI-Nspire.
Both qualitative and quantitative evidence showed the Traditional TI-84 group had fewer changes in attitude and content knowledge than everyone else combined, suggesting the need to change how we teach data analysis. Problem/project-based learning, if introduced gradually, may prove to be an effective teaching/learning educational practice.
Further exploration needs to match students’ technological and data analysis proficiencies when determining readiness for student-centered learning that expects students to be calculator proficient and comfortable with basic quantitative procedures such as finding measures of central tendency and variation.

A qualitative study in one algebra geometry III classroom of students using TI-Nspire CAS showed TI-Nspire CAS  had a positive effect on students’ understanding of solving equations, using parentheses, and understanding equivalent operations.

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.

While it seems clear that instruction on both procedures and concepts is important in mathematics education, the relative importance of each and the order teachers should use each to build instruction with handheld technology such as graphing calculators is still unsettled.

A quasi-experimental study of graphing calculator use in grades 7-10 of one German state showed 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%

The study focused on three research questions:
- What is the effect of the use of the TI-Navigator technology on eighth-grade Algebra I students’ achievement in the areas of graphing, solving systems of equations, and solving linear equations?
- What is the effect of the use of the TI-Navigator technology on eighth-grade Algebra I students’ attitudes and beliefs about the use of calculators and other technology in mathematics, specifically algebra?
- What is the effect of the use of the TI-Navigator technology on eighth-grade Algebra I students’ interactions during mathematics class?
Two eighth-grade algebra classes were matched in terms of gender and achievement levels by a random process used at the project site. One class was randomly selected to be
the control group and the other designated as the experimental group. The control group class used calculators as appropriate to their regular curricular program but were not
given access to the TI-Navigator technology. The experimental class used the TINavigator
technology daily for two months during the two chapters designated in this study. The calculator used in both classes with the TI-84 Plus Silver Edition. Each student was assigned a calculator for use at school but may not have had access at home.
Pre-and post-tests on content knowledge were administered at the appropriate times concurrently with an attitudinal survey. Daily classroom observations were also conducted and recorded using an observation protocol.
This summary reports the statistical data taken from the two administrations of the content knowledge tests. The description of how the appropriate statistical procedure was
selected is included.