The original Richardson MathForward Program analysis for 2005 – 2007 is reviewed here and supplemented with a revised analysis to account for certain assumptions not addressed previously. While the general conclusions have not changed from the original report, they are expanded upon here with revised values that are believed to be a more accurate representation of what was happening to students in the study between 2005 and 2007.

With the TI-Navigator system, 27% percent more students scored in the 90% range on the New York State Regents Math A for 2007, when compared to the same teacher’s non-TI-Navigator system class in 2005

Pre-/post-comparisons showed gains in perceived experience from the beginning to the end of the course. However, the number of students who felt nervous about the prospect of using graphing calculators increased.

I can look at the Navigator screen and I am able to diagnose the problem areas and fix them for the individual(s) before moving on in my content.  And, … a 100% made gains on the FCAT

Formative assessment with TI-Navigator has helped this teacher to deal efficiently with misconceptions, and to use class time more efficiently.  In the process, his thinking about teaching and learning has evolved

What follows is a careful, detailed attempt on our part to provide the NMP our views pertaining to the issues we believe you should consider. These views are based on our experiences, review of available research, and lessons learned. We understand that they are not grounded in scientific research, though, in certain circumstances, significant research, some of which we are sponsoring, is uunderway. We would be pleased to report results of further research as it is completed. The key point we want to make, however, is that to achieve and sustain student performance improvement, we have learned that key elements of the mathematics education system must be addressed in a coherent, integrated way, and there is no “silver bullet” focused on a single system element.
We understand there is not fully developed scientific research to prove this hypothesis; rather, it is an observation from decades of experience and involvement in the field. Our hope is that you will uncover and publish, if it exists, scientific evidence on the proposition that systemic reform is necessary as well as the proven components of a comprehensive system that will effectively deliver mathematics education and improve student mathematics performance. If such scientific research does not currently exist, we strongly recommend that the NMP make such research a matter of the highest priority in its conclusions and report.

Canton is a case of a district where differences in outcomes by grade level appeared to be correlated with levels of implementation. Higher levels of implementation were linked to better outcomes, providing some support for evidence that interactive teaching methods are an important ingredient in the program’s success. In addition, Canton was an example of a district where, despite small numbers of students, MathForward had a positive, gap-closing effect for African American students. At the same time, the differences between gains in 2007 to 2008 may have been caused by factors other than MathForward, such as events that took place during the 2007-08 school year.

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.

The pattern of results was different for the two grades studied. In seventh grade, the losses made by MathForward students were lower than the losses made by comparison students. However, the differences were no different from chance.  In 8th grade, MathForward students significantly outgained comparison students. In neither grade did student gender or ethnicity affect student gains. It is difficult to interpret the differences in the results for the two grade levels in terms of implementation. The four MathForward teachers also provided instruction to comparison students, and they had access to the technology in comparison classrooms. At the same time, one of the seventh grade teachers did not receive training and was gone for most of the year, which could have explained differences in the results for different grade levels.

Euclid is a case of a district where implementation was strong, but where the sample size of the MathForward group was too small to detect significant effects.  MathForward and comparison students were roughly comparable, and implementation was strong in the classroom and well supported by district staff and coaches. But to show significant differences between the MathForward and comparison students, the differences between the two groups would have needed to be between 6 and 9 points. Those differences are large, relative to differences produced by interventions studied in education and that have been judged to be successful.

Springfield is a case of a district where implementation was strong, and where the sample size of the MathForward™ group was large enough detect statistically significant effects, so the results are not due to chance. At the same time, the differences between gains in 2007 to 2008 may have been caused by factors other than MathForward™. In addition, instability in estimates of gain scores from year to year make it difficult to determine whether measurement error or differences in test difficulty from year to year are the cause of the observed change.

Levittown is the case of a district where implementation was high and in which one of two grade levels’ scores were higher for MathForward students than for comparison students. The differences in outcomes may have been due to several reasons, including the fact that implementation was lower for
two 10AXBX teachers. Although the sample sizes were small for both groups, the observed effects were large enough among the 9AX students to be statistically
significant.

All schools increased time for mathematics instruction for
participating students.
-Teachers’ professional development
experiences were deep, extended, and varied in format.
- Most schools did not provide common planning periods for
participating teachers.
- Teachers and students found the TINavigator™ technology contributed positively to teaching and learning.
- When using TI-Navigator™, teachers used its formative assessment functions most often.
-Teachers used assessment data to adjust the pace of their instruction

Existing research suggests that integration of graphing calculators can improve student conceptual understanding, attitudes toward math, and retention in college level studies in math and related fields.

In an qualitative 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.

This report describes an analysis of an intervention with the goal of enhancing mathematical understanding through the use of graphing technology, in-classroom networks and daily problem solving. The intervention has been implemented in several 7th and 8th grade math classes in a Texas school district.  This analysis examined changs in the TAKS math scores of students receiving the intervention compared to students not receiving the intervention in the academic school year 2005-6. 
These results for all four models presented, indicate that students that are in the treatment group,
For Analysis One, results indicate that being included in the study group tends to predict an increase in the math TAKS assessment. The first model (Table 3), indicated that the estimatemath TAKS NCE score tends to be about 5 NCE points greater in gains than comparison students. However, in the second model (Table 4), the study group change was not statistisignificant, although the coefficient was positive, indicating that scores for the study students increased slightly compared to other 7th and 8th grade students in the district.

In Analysis Two, the third model (Table 5), indicated that the estimated math TAKS NCE score owever, in the fourth model (Table 7), the treatment group change was not statistically significant, although the coefficient was positive, indicating that scores for the treatment stend to increase compared to other 7th and 8th grade students in the district. In this model there was a discontinuity observed at the cutoff, but the treatment group growth was not significantlydifferent from the other 7th and 8th grade students in the district.

Although causal conclusions can not be made, the students in the treatment program appear to have benefited the intervention and from the key components which included: extended learningtime, use of technology to motivate and enhance learning opportunities, provision of common, aligned assessments, increased teacher content knowledge, and development of high expectationfor all students. The goal of this systemic intervention was improve mathematics achievement. Results indicate that students who received the intervention had on average, higher math TAKSscores that the students not receiving the intervention

The research design that utilizes Regression Discontinuity Design (RDD) was applied to produce a “gold standard” study without major disruption of normal school work. These research results indicate that applying an intervention program to those students most in need (students not passing the math TAKS), can produce both high quality research results and benefit studentneed.

Based on these analyses and given the goals of the program, the Richardson Model for improving math TAKS results can be considered a success. In addition, the successful uregression discontinuity design and the consistency in the increases shown under both the regression discontinuity analyses and Ordinary Least Squares analyses speak to the effectivof the statistical approaches advanced in this research project.

Further examination of the district administered Benchmark tests will be made. From this researchers hope to better understand the connection of program implementation, student progress toward learning objectives, and test performance. Finally, larger “N” or number ostudents involved in future projects may help some of the positive trends observed in this preach the level of being statistically significant.

On October 12, 2006, Texas Instruments (TI) provided comments to the National Math Panel (NMP) on a variety of issues related to its charter for the improvement of mathematics education. Since then, the NMP made the decision to consider technology and its role in math instruction.

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

An experimental study on CAS in a core calculus course found:
-- The experimental group attained a higher mean score than the control group on thirteen of twenty items.
-- Among the twenty items, the only significant differences in mean scores (p < 0.05) were found in eight of the items favoring the experimental group.

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.

This is the interim report of a two-year study of TI-84 + TI-Navigator in two schools of the Toronto Catholic Board system,  grade 10, academic and applied tracks.  A quasi-experiment showed greater achievement for the academic classes than similar non-TI-Navigator classes.  However, there was no difference for applied math classes.  Final report will be published in 2009.

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.

Year 1:   Pilot results in the middle school where MathForward was implemented showed increased teacher content knowledge, including knowledge of patterns, functions and algebra. Teachers’ self-reports included:
-their teaching effectiveness and techniques improved from mid year to year end
-use of TI-Navigator system increased student participation and reduced behavioral problems
-students’ algebra readiness increased