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.
|MathForward, Mathematics Education, Urban, Underperforming, Systemic Interventions|
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.
|MathForward, Richardson ISD, TI-Navigator, TI-73, Graphing Calculators|
In this systemic improvement program, district-wide proficiency on the standardized state test climbed steadily during three years from 39% to 62% in both 7th and 8th grades.
|Case Study, TI-Navigator, Graphing Calculator, MathForward, Algebra, Grade 7, Grade 8, Pre-Algebra, Cognitive Tutor|
Low-cost, portable classroom network technologies have shown great promise in recent years for improving teaching and learning in mathematics. This paper explores the impacts on student learning in mathematics when a program to introduce network technologies into mathematics classrooms is integrated into a systemic reform initiative at the district level. The study conducted compares the performance of middle and high school students who were participants in the Texas Instruments’ MathForwardTM program to students in the district not in the program. Results indicate that students at two grade levels who were in the program made greater 1-year gains in mathematics achievement than students not in the program.
|MathForward, TI-84, TI-73, TI-Navigator, Middle School|
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.
|Mathematics education, technology, graphing calculators, mathforward, national math panel, research|
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.
|MathForward, Canton Local, TI-Navigator, TI-73, Graphing Calculators|
Previous work has identified Ten Components of Effective Schools which were often associated with schools and school districts whose students were achieving above average academically. The main purpose of this study was to determine if a questionnaire-based data gathering process could capture information sufficient to test the efficacy of these Ten Components upon mathematics performance in elementary and middle schools. That is, can a short questionnaire filled out by teachers and administrators adequately capture sufficient information about such characteristics as administrative practices, curriculum alignment and professional development to test whether different degrees or quality of implementation of these practices actually makes any difference in educational outcomes at the school or school district level?
Information was obtained from 828 teachers in 104 schools located in 18 school districts across three states—California, North Carolina, and Texas. Several districts in each state and several schools within each district were selected which had large proportions of economically disadvantaged students. In addition, it was attempted to get a mix of districts which exhibited either higher than average or lower than average performance among the majority of their campuses, using a criterion described in the paper.
Correlation and linear regression analyses were used to see which of the Ten Components were associated with the more successful schools, leaving aside district influence. Using Hierarchical Linear Models (HLM) analysis, the district-level aggregates derived from the survey data were used to determine which of the components were most strongly associated with higher than predicted performance among the school districts in the sample.
Strong and consistent correlations were found between school-wide average student math performance and the degree of implementation of several of the Ten Components. The survey results were even more effective in explaining variations in the average math performance of entire school districts, even when correcting for differences in the proportion of economically disadvantaged students.
The results were weakest based upon data for North Carolina. Reasons for this are discussed.
|Mathematics Education, Components, MathForward, graphing Calculators|
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.
|MathForward, North Brunswick, Algebra, TI-84, TI-Navigator|
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.
|MathForward, Brentwood, TI-Navigator, TI-73, Graphing Calculators|
The study had adequate power to detect small effects, and comparison groups were similar enough to the program students to infer that the analysis reflects differences in gains attributable to the program as implemented. But Dallas is a case of a district where limited implementation of interactive pedagogies with TI-Navigator may have reduced the effectiveness of the program. In addition, staff turnover at one DISD school may have reduced implementation quality.
|MathForward, Dallas ISD, TI-Navigator, TI-73, Graphing Calculators|
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.
|MathForward, Euclid OH, TI-Navigator, TI-73, Graphing Calculators|
The results were different for the two schools in the study. At Jackson Memorial Middle Schools, students in MathForward outscored comparison students in 2008, but the difference may have been due to chance, because it was not
statistically significant. By contrast, at Jackson High School, comparison students outscored participating
students, but these results may also have been due to chance and participating students had lower scores than comparison students in 8th grade. In the high school, impacts would have to have been large to achieve statistical significance, due to small sample sizes. There were no significant differences for boys or girls for either school, and there were not enough low-income students or students of color from the district to analyze results for these two groups of students.
|MathForward, Jackson OH, TI-Navigator, TI-73,Graphing Calculators|
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.
|MathForward, Springfield OH, TI-Navigator, TI-73, Graphing Calculators|
West Palm Beach County is a case of a district where implementation was not particularly strong, and where there was no evidence of program effects on achievement. MathForward and comparison students were roughly comparable, and the sample size was adequate to detect effects of the program. One possible explanation for the results was that the district’s schools transformed the intended design of the program in ways that may have limited its effectiveness.
|MathForward, West Palm Beach FL, TI-Navigator, TI-73,Graphing Calculators|
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
|MathForward, Levittown NY, TI-Navigator, TI-84,Graphing Calculators|
In year 3, the overall gains made in mathematics by MathForward™ students on the Texas Assessment of Knowledge and Skills (TAKS) were significantly greater than for comparison students. These students differed from the program students in that they were higher-achieving and less likely to be minority students. The gains of MathForward™ students were greatest in 7th grade, relative to the 8th grade and Algebra 1 students that participated. African American students in the program made greater gains than African American students not in the program, resulting in decreasing the achievement gaps for that group. Among the MathForward™ students, 55 percent of students scored proficient or higher in mathematics in spring 2008, compared to 48 percent the year before. These findings are consistent with achievement gains in previous years for participating students
|MathForward, Richardson, RISD, TI-Navigator, TI-73, TI-84,Graphing Calculators|
All schools increased time for mathematics instruction for
-Teachers’ professional development
experiences were deep, extended, and varied in format.
- Most schools did not provide common planning periods for
- 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
|MathForward, TI-Navigator, TI-73, TI-84,graphing Calculators|
Prior to the project, 93% of teachers indicated that they never used supplemental materials in algebra or
geometry in the classrooms. Since purchasing the TI-Nspire calculators for all students, daily classroom
usage of the equipment increased to 77%. Sixty percent of teachers said their students use the calculators
for in-class inquiry-based explorations using the calculator’s scientific functions. Additionally, math
benchmark test data show that the classes furthest along in implementation (utilizing the technology most
consistently) demonstrate the greatest score gains.
|MathForward, TI-Nspire, TI-Navigator, STEM, DoDEA, Clover Park, Case Study, Science|
At RISD, 7th and 8th grade students who used TI MathForward achieved higher scores on the Texas Assessment of Knowledge and Skills (TAKS) Mathematics than similar 7th and 8th grade students who used other mathematics programs during previous years. This study found evidence that the strongest application of MathForward was at grade 7 and a positive, but smaller, result was found for grade 8. The study also found that 9th grade Algebra I students who used MathForward scored lower than a similar group of 9th grade Algebra I students from previous years. While there is no evidence that 9th grade Algebra I students achieve higher after having participated more years in MathForward, students appear to achieve higher if their teachers have more experience using MathForward.
|MathForward, RISD, Richardson, TI-73, TI-84, TI-Navigator|
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.
|MathForward, TI-Navigator, TI-73, Richardson ISD, RISD,Graphing Calculators|
In conclusion, under OLS analyses the study intervention is effective in raising both Type 1 (students who failed the previous year TAKS) and Type 2 (students who passed the previous year TAKS) students’ mean NCE scores. This lends significant support for the versatility and inclusiveness of the intervention when it comes to classroom use. Due to this increasing of the Type 2 Study students’ scores and lack of growth in all other Type 2 students, OLS regression analysis always yield significant results, but regression discontinuity often did not. The closer the Type 1 Control students were to the Type 1 Study students, the more likely the regression discontinuity would fail to find significance.
Future work, to validate some of the implications of these analyses, should examine what is happening in the Control classes. This is especially true for the Control 2 classes which in this analysis resemble the Study classes the most at the Type 1 level.
Regression discontinuity analyses did show significance at the district level comparison. In general across OLS and RDD analyses, when significance was found the effect of the intervention was in the four to six point range for improved NCE score on a 100 point scale. Even when significance was not reached, the results often were trending in this range. This convergence of results across complementary methodologies lends further credibility both these findings and to the methodologies developed for these analyses.
To conclude, the overall results indicate that the MathForward intervention resulted in scores of students below passing in one year improve their scores by 4-6.5 points in the subsequent year.
In contrast to other forms of intervention that result in some improvement in outcome for underperforming students but at the apparent expense of students scoring above the passing level, the results of this study suggest scores for all students in classes using the MathForward program improved. All students appeared to benefit from participation in the MathForward program.
|MathForward, Richardson ISD, RISD, TAKS, TI-Navigator, TI-73,Graphing Calculators|
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.
|MathForward, National Math Panel, Evaluation, Research Review,Graphing Calculators|
The overall model results indicated that MathForward participation was associated with significantly higher gains in mathematics achievement, when compared to students in the
district not in the program. Grade-by-grade analyses suggest that gains associated with being assigned to the program were primarily in Grades 7 and Grade 8. Furthermore, except for Hispanics in 9th grade, there was no evidence from this study that achievement gaps were closing for students in the program, relative to students not in the program. In grade 7, implementation rates were higher than in the other grades, suggesting one possible explanation for this pattern of results. Teachers made more frequent use of the most powerful TI-Navigator tools in this grade level, and 7th grade teachers also were =more likely to adjust their instruction on the basis of formative assessment data collected using TI-Navigator than were teachers in other grades. The fact that the treatment effect was strongest in this grade suggests that the achievement gains are at least partly attributable to the program. These results are suggestive of the promise of the intervention, but the models tested here do not permit us to conclude that we have unbiased estimates of program impact. There were significant differences between the two groups with respect to both student background and prior achievement, and propensity score matching did not yield groups with enough overlap to create a matched comparison group. The use of gain scores can mitigate potential effects of differences, but the fact that program students had more room
to grow may have affected the results. Thus, we cannot conclude that the significant gains observed in this study were caused by the program. Because of the threats to internal validity, there are limits to both generalizability and potential significance for policymakers beyond RISD. We know little about how the achievement gains of low-performing students compared to those of students with similar profiles as program students, since so many students in the district participated that a matched comparison group was impossible to construct. Comparison groups from outside the district may yield better estimates of impact in future years, but these students may
not share enough of the same policy and district context to yield valid results.
The limitations of the study do not prohibit either TI or RISD from drawing lessons from the study. The relationship between implementation and gains suggests the promise of the
program for high-implementing classrooms; it also suggests the need to understand how to support such implementation in the future. For RISD, the gains made by students are
confirmation of its policy and approach: MathForward students are making significant gains, at least in 7th and 8th grade. The poor results in 9th grade suggest, furthermore, that the district take a closer look to uncover why these results were not as strong as for the other two grades.
|MathForward, Richardson ISD, RISD, TI-Navigator, TI-73, TI-84,Graphing Calculators|
Summarizes results from:
Richardson ISD (RISD)
Dallas ISD (DISD)
Palm Springs, FL
|MathForward, TI-Navigator, TI-73,Graphing Calcultors|
Based on teacher surveys and measures of teacher math knowledge, cumulated across all districts:
-There was evidence of a positive association between teacher math content knowledge and student performance on statewide tests
-The top benefits of TI-Navigator™ technology, from most teachers’ point of view, were more immediate feedback about what students know and can do and enhanced student conceptual understanding of mathematics.
-Teachers varied in the extent that they engaged students in extended discussion of their ideas. When they did engage students, most often discussion was part of whole-class instruction or review.
-Most teachers did use the TI-Navigator displays in their class so that students can see the distribution of responses to problems in class. Some used the data to speed up or slow down the pace of instruction.
|Teacher Pedagogical Content Knowledge, TPCK, CKT-M, MathForward, TI-Navigator, TI-73, TI-84,Graphing Calculators|
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
|MathForward, TI-Navigator, TI-73, Richardson ISD, RISD, TAKS, Graphing Calculators|
Year 2: Jr. High program expansion showed:
-Growth in teacher knowledge of number & operations was positively associated with the TAKS performance of their students.
-Teacher self-reports of confidence improved.
-Teacher self-reports of collegial support remained high across the year.
|MathForward, TI-Navigator, TI-73, RISD, Richardson ISD,Graphing Calculators|