Mathematics Curriculum Education

Mathematics Curriculum Education

One aspect of math instruction and instruction in general that has been particularly important with high stakes testing reform is staff development and system support of staff and students to improve outcomes and/or balance information offered by high stakes testing and ultimately improve mathematics teaching practice. This emphasis has, as of yet gone relatively unexamined, beyond the actual high stakes test results themselves. For this reason the results of the findings section of this work are important and meaningful, especially as we embark on the future, with a new presidential administration along with a changed congress and changes in local officials, who may have significant amendments to make to the educational standards of the nation. In short the new administration, on all levels, must understand what about the NCLB and other mathematics reform movements are effective and what might need to be changed or improved. Without the input of educators and students such an assessment is inadequate to say the least. (Minkoff, 2001, p. 20)

This work develops a quantitative examination of the level of such reform development through a series of questions associated with such development. The two main intentions of the work were to; (1) identify reform-related practices in mathematics instruction that have increased, decreased, or not changed since the implementation of high stakes testing, based on educators' perceptions.; and (2) determine educators' perceptions of the effects of reform-related practices on improving student achievement since the implementation of high stakes testing. In the work 134 educators, 2/3 teachers and the remainder math lead teachers and administrators, across a broad demographic that represents well educators in general, were polled and the results support overall math reform and relatively positive perception of reforms (Table 1).

To answer the initial question 17 reform related questions were rated on a seven- point scale (1 = Large Decrease to 7 = Large Increase). As is to be expected district items with the largest increase ratings were "Staff development activities (M = 5.81)" and "Performance-based assessments (M = 5.72)." These reform activities support furtherance of staff effectiveness, through continued education as well as informative educational practices to allow staff to fully utilize, understand and balance the information given by high stakes tests, i.e. performance based assessment. The results in short stress that the need for additional training to implement the new standards-based testing, to elicit more positive results on such tests was evident from the beginning and that educators also recognized the need to balance information gleaned from high stakes testing with additional performance based assessment.

District items given the smallest increase rating were "Enrichment programs (M = 4.10)" and "Summer school programs (M = 4.22)" (Table 2). Again, as was to be expected the lowest increased ratings support the fact that high stakes testing has at least to some degree reduced the ability of educators to develop programs that go beyond the teaching and testing of traditional materials to increase enrichment programs, likely as a result of the need for more education of educators with regard to reforms. Additionally, it could be seen as a positive aspect of practice or the summer school programs in these particular schools could have been adequate to begin with or the program changes have increased standard school year learning requiring less need for supplemental instruction in the summer, as such programs have been only marginally increased since the inception and application of high stakes testing took hold. Table 3 results seen above demonstrate a second aspect of the first intention noted in this section and reflect classroom practice program experiences; the highest on the same seven-point scale in table 3 were "Align instruction with frameworks (M = 6.40)" and "Support district curriculum in mathematics (M = 5.97)." Classroom items given the smallest increase rating were "Use lectures to present content (M = 3.72)" and "Complete long-term projects (M = 4.19)" (Table 3).

Yet, more importantly the assessment also responded to the idea that mathematics instruction has had to align itself to alternative methods, such as the development of "real world" math examples and other supported challenges for improving the content and context of math instruction, (Incorporate real world activities into math instruction 5.49 (Table 3) while only limitedly increasing the utilization of traditional methods, such as lecture to impart instruction. Mintrop's concern that teaching under duress might eliminate creativity seems not to be supported by the results of the perceptual analysis as teachers, for the most part seem to be stressing the need to look for alternatives, in addition to high stakes testing reforms to achieve greater success with instruction, rather than falling back on lecture-based traditional instruction. (2003, p.17) Some marked decrease in the improvement of long-term project goals was also seen, but all classroom reforms were improved as all 33 classroom practice elements showed marked increase rather than stagnation or decrease, which supports reform implementations. (Turchi, 2002) This emphasis on increased staff development, which is seen in the statistical analysis of this work does not necessarily support a narrowing of teachers duties or abilities, as reforms have been implemented. (Fashola & Slavin, 1998) it seems that the alignment sought by Bolt and others, created through increased teacher learning and creativity could be realized even in the high stakes testing environment if improvements continue to elicit teacher involvement and continued education. (Bolt, 2003, p. 32)

The additional statistical work to be found in this paper has to do with the basic research intention 2, which emphasized the varied perception of both educators with regard to reform measure effectiveness post high stakes testing implementation in the classroom, with the exception of the overall statistical work that addressed district and state assessment score changes. (in such (figures 1,2,3) the results showed only marginal improvements in nationally recognized assessment scores, since the implementation of high stakes testing.)

Table 5 displays the one-way ANOVA comparisons for the district and classroom increase factor scores for teachers (n = 90), math lead teachers (n = 13) and administrators (n = 31). Significant differences were noted between the three groups of educators for both the district increase factor (p =.009, eta =.26) and for the classroom increase factor (p =.008, eta =.27). Scheffe post hoc tests found a similar pattern of results for the two factors scores: no significant differences were noted for the perceptions of the teachers compared to the mathematics lead teachers nor for the mathematics lead teachers compared to the administrators. However, in both cases, teachers gave lower increase ratings than did administrators for the district increase factor (p =.009) and for the classroom increase factor (p =.008) (Table 5).

The initial goal was to determine if reform perceptions were in some way determined by the demographic attributes of educators as well as other factors or if such was independent of demographics and therefore universal to educators (Table 4-13). In general the role of educators, i.e. classroom teachers, math lead teachers and administrators showed differences in perception based upon the several factors indicated as classroom teachers had a more negative perception of the effectiveness of reform while administrators showed a higher degree of positive perception of change and math leads fell somewhere in the middle, while being more aligned with other classroom teacher perception.

Discussion

Overall the results of this work have both positive and negative outcomes that are telling of the need for greater understanding and greater alignment of instruction with goals. Teachers and programs are implementing instructional and broad reforms and are still out on the subject of their effectiveness in the classroom, and especially with regard to students already on the fringes of learning, i.e. special needs students of every discernable type (Table 12-13).

This differences in perception, though not demographic but role-based shows that there is still work to be done to align high stakes testing reforms with classroom and instructional effectiveness, per the perception of real life teachers in the classroom, while administrators would like to assess the reforms as effective, even if doing so is premature. It is assumed that such perception has to do with role differences as well as administrator buy in of reform methods, that classroom teachers are not privy to, as well as real differences in perception based on real differences in the classroom. It was to be expected that change would have a different buy in, given different roles of educators, especially considering that each has a different role in implementation as well as different information regarding the reasoning and standards associated with reform. While administrators may have had at least some input in the reform planning process, classroom teachers are much less likely to have had such an experience. Additionally, administrators are often "sold" on broader concepts of reform, in mathematics and elsewhere while teachers are then expected to accept changes as a result of other peoples' buy in of them. This can clearly be implied from the results of these perceptual assessments of reform implementation, as administrators accept the change as overall positive while teachers are withholding judgment until they have more concrete, real life examples of the positive aspects of such reform, such as positive student outcomes, represented by increased student display of knowledge on performance based as well as test results.

The foundations of high stakes testing indicate that their intention is to formulate change that is traceable and transparent. Accountability is essential to outcomes but instruction must be aligned to the needs of students and educators and most importantly must be inclusive of the perceptions and perceived needs of real life classroom teachers. Tracing the effectiveness of high stakes reforms and reforms that would be considered the fall out of such is essential to the development of alignment between curriculum and test results. (Bolt 2003) These changes cannot under any circumstances be judged solely on the perceptions of administers, as has been shown by this work administrators give a great deal more positive assessment of reform, prior to the acceptance of such reform as positive by real world classroom teachers. This is especially true with regard to those students who are clearly already at a disadvantage in the system, a finding that supports McNeil (2000) in the fact that high stakes testing reform has a tendency to aide only advanced and "normal" students while it may leave remedial students lagging.

No matter the outcome of testing, or the reform that achieves such outcomes the most important voices associated with it will; remain real classroom teachers who have the capacity to see, implement, learn from and hopefully develop creative systems to aide students not only in their ability to effectively take tests but to effectively learn basic and abstract concepts in mathematics instruction. This voice is essential in eliciting real change and cannot be ignored in any sense.

It is clear that both good and bad outcomes have ensued as a result of the accountability movement in mathematics reform. Teachers and others have increased the amount of continuing education and most importantly have sought alternative (performance based) assessment tools to balance the challenges of "teaching to the test" and to come to a greater understanding of how to implement and assess changes most effectively. Sadly, as with many reforms those who are already challenged stand to see the least improvement in both test scores and basic understanding of material as perceptions of these 134 educators indicate that only above average and average students are benefiting from high stakes math reform, while marginal students are not showing a great deal of improvement, if any.

Mathematics proficiency has often been seen as the litmus test for the effectiveness of any educational system, with and without reforms implementation. Student proficiency in math is essential to the development of students who can succeed in many other applications, both real world and academic, even when such success is seen as only marginally necessary by such students. Teacher perception, student perception, real proficiency and real test scores are all essential aspects of judging the effectiveness of any mathematics instruction. The influence of high stakes testing on awareness of progress is an unexpected positive outcome of the high stakes reforms, while fear of leaving behind already challenged students is the most negative outcome of reforms Either way, without the perceptions of real teachers in the classroom on a daily basis such understandings about the need for reversals or even further changes is impossible.

Conclusion

Though change is an essential aspect of the human condition, and change often elicits positive outcomes all change is not wholly positive. Teacher perception is such an essential aspect of mathematics or any educational reform that the need to assess it and then respond to it is crucial to a greater understanding of real classroom experiences. Through the accountability movement mathematics has clearly one through a transformation, and as this assessment demonstrates teachers are withholding judgment regarding its effectiveness and its measurements. Some very positive aspects of resistance and acceptance have been attained as teachers and their support systems implement greater creativity than was initially expected by achieving more continuing education and creating alternative assessments that can elicit greater breadth of understanding of real student achievement of knowledge attainment.

The importance of teacher buy in of reforms is essential but teachers clearly have right and reason to withhold judgment regarding reform until they know for sure that the changes implemented will really result in improvement of student outcomes and better essential knowledge of mathematics. Though this assessment is clearly topical, continued long-term assessment of teacher perception is essential to understanding how such changes will effect classroom applications and student achievement, especially once the teacher learning curve regarding the implications and applications of reform have been reached through further instruction and utilization of reform principles.