# Framework for Implementing the Z Mathematical Model to a Six Grade Class Term Paper

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positive outcome in the educational progress for the students resulting from applying the Z. Model framework. In Mr. Zander's classroom, the average improvement in test scores is 16.75 points. The is the rise in test scores resulting from the students taking the same standardize test, once at the beginning of the school year, and a second time after 6-7 months Z. Model application.

The baseline group data was taken form another 6th grade Mathematics' class, taught by Mr. Valree. The same test was administered at the same intervals. The difference was that Mr. Valree's class experienced standard teaching methods. The average improvement for this baseline class is only 3.25 points. The level of baseline class's improvement should be expected for no other reason that the students are completing the same test. It would be expected of the students taking the same test for these students to achieve higher scores on their second attempt. This result brings into question whether of not the students in the baseline class are experiencing any real learning during the school year.

Looking more closely at the results from Mr. Valree's class, it can be seen that his score improvement is significantly affected by the performance of 2 students. If in Mr. Valree's 5th hour, the 2 exemplary improvements are put aside as aberration in the data, the average change in the 5th hour class would be 0.6, bringing the average improvement of all students to 1.4 points. When taking into consideration that the students are taking this same test at different periods of the year, and that it can be expected that they would perform better in the second attempt, the question remains to be answered if the impact of the standard educational process during the school year was of no positive impact on the students educational progress. According to Bransford et. al. proponents of educational reform highlight the importance of creating instructional environments that encourage students' active involvement in the learning process. To be so involved, students must construct knowledge, evaluate the products of their work, and engage in the design of solutions to authentic problems. (Bransford, et.al. 1991). Their analysis of the research evidence leads to conclusions those students' thinking skills and attitudes are enhanced when they collaborate in the solution of authentic problems. The progress of the students undergoing the Z. Model clearly are being encouraged and support to create the new learning pathways and construct knowledge through the use of a project-based learning, and with the additional support of the community, particularly their parents or care givers. The students in Mr. Valree's class are not making the connection between the text materials and concrete application and understanding.

A second conclusion that can be drawn form this data, and the as an evaluation of the Z. Model is that the experimental group of students not only improved significantly, but also improved consistently. The average change improvement of Mr. Zander's classes was not due to a handful of extraordinary students who benefited from the teaching framework. Forty three out of seventy one achieved double digit improvement; 29 out of 71 demonstrated an improvement of over 20 percentage points. This is significant, if not an outstanding change in the level of academic performance. By addressing a spectrum of educational needs the students were motivated, engaged, and equipped to participate in the educational process. These students, possibly for the first time, make real time connections between their class text material and the real world. Through a project based approach, the math principles became meaningful to the group of students working on a problem, and therefore became meaningful to the individuals in the group.

Much research has been undertaken to evaluate the effectiveness of multi-media projects and equipment in the classroom. Bransford et. al. contends that educational multimedia is potentially powerful tools for constructing knowledge, especially when used in collaborative project-based instructional environments, or multimedia design projects. Their studies in the area of social studies review evidence about the efficacy of multimedia design projects in promoting students' construction of knowledge, thinking, and problem solving, and discuss some potential challenges to the efficacy of this approach. With the invasion of high tech movies, video games equipment, and personal gaming systems that have become an integrated part of the student's life, utilizing multi-media technology is a natural evolution of educational equipment.

The Z. Model, because of the interaction of the 4 domains and the constant positive pressure placed on the students toward educational improvement could be called a low tech multi-media approach to teaching. High tech multi-media equipment utilizes sound, color, the intrigue of high tech gadgets, and a fast moving environment to engage the players, or learners mind. The high tech multi-media engages the student, and with the addition of headphones, the student can become engrossed in the entire high tech multimedia world-scape. The Z. model engages the student on a multi-media approach also. The student is grabbed in the classroom with a project-based work team. He is given objective standards, solid goals he is required to meet. His class mates are engaged in the same pursuit. He is met by his parents who, on another educational 'multi media' front (the home); engage the student in the pursuit of the same goals. The tools are different between a computer with a power point lesson, but the approach, and therefore the results, are similar. In the advertising world, successful advertising campaigns are measured in viewer impressions. Again, the goal is to co-opt the consumers, attention through many mediums to deliver a consistent message. If we could combine these terms, media impressions and multi-media, the Z. Model could be similarly be called a multi-impact teaching model. It is not multi-media as the term is understood, but the goal is to develop inclusive scaffolding around the student in order to enable and encourage him to learn.

In comparison, the baseline group demonstrated a wide range of results. While many of the group improved including improving, and regressive performance. Eighteen out of fifty nine students who took both tests demonstrated regressive performance. These students scored lower on their second attempt on the test. The overall performance is "all over the map." This is a disturbing trend, and the continuing falling rates of academic achievement have been the subject of national focus. A seemingly endless stream of reports from prestigious state, regional, and national commissions (e.g., National Commission on Excellence in Education, 1983; National Commission on Social Studies in the Schools, 1989) lament the failure of educational institutions to prepare our children for the challenges of life. Most advocates of educational reform would probably agree that schools should prepare students to contribute to constructive, personally satisfying, and socially valued activities in a representative democracy. There is much less agreement, however, about the specific strategies and educational processes that are proposed to achieve this goal. For some, the focus is the acquisition of basic skills, for others, it is a national curriculum or standardized assessments, and for yet others, the student's capacity to think critically and analyze information is emphasized (Cherryholmes, 1990; Engle, 1990; Epstein & Evans, 1990; Nelson, 1990).

A national cry within the academic community for 3 decades has been for smaller classes and more money to spend on education. While the smaller classes have been achieved, it has been measured that the school districts with the highest spending per student, (Washington DC and New York) have some of the poorest performing students. In the urban setting, the ability to increase funding for schools which are already demonstrating suffering educational performance rates is very restricted. The solution is for teachers to find a method with the resources they have to engage their students, and increase their educational success rates. The Z. Model is one approach that appears to do just that.

The discipline of education is currently enjoying the unprecedented attention of parents, policymakers, and public officials. While the word 'enjoying' may be a misnomer for a process which is identifying a failing system, the positive outcome is that the educational slide is slowing, and schools are experimenting with procedures which will reverse the course of educational decay. This work is predicated upon the premise that education should encourage students' disposition toward engaged thoughtfulness and reflection (Dewey, 1916; 1933; Wiggins, 1993), and that it is possible to design learning environments that encourage students' construction of knowledge and active problem solving.

Bransford, Goldman, and Vye (1991) offered a compelling account of the issues that have shaped views about thinking and problem solving over the last decade. First, many students score poorly on tests of problem solving, essay writing, reasoning, experiment design, and the like (e.g., Gentile, 1992; National Assessment of Educational Progress, 1981; National Commission on Excellence in Education, 1983). Second, business leaders have serious concerns about workers' reading, writing, speaking, learning new skills and adapting old ones for use in the workplace, using quantitative skills to manage and produce job-related information, and assessing and generating arguments and explanations (Resnick,…[continue]

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