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Alternative Instructional Tools

An examination of two [City] schools, [name] High School and [name] Elementary School resulted in insights into the connection between math curricula and poor performance by students on standardized testing. The high prevalence of students lacking access to resources and adequate study tools seemed to be reinforced by constraints made on teachers were the exceptional distance between national criteria in performance and actual student competencies in math. There was also a measure of Vygotsky ZDP "imitation" that bespeaks more of the redundancy in failure in underserved classrooms than the instrumental application of learning methodologies. The observations led to the furtherance of the query into math competency assessment, and especially the potential of alternative learning tools in the promotion of student performance where learning disabilities are present in high number.

Math Education Assessment & Policy

Since the ratification of the No Child Left Behind Act (NCLBA) in 2001, the US education system has been under significant pressure to provide evidence of equity in education. If the rationale behind standardized learning is to promote student test performance, mathematics is perhaps the most critical consideration in student performance within the core knowledge domain. Measured assessment of student achievement for all students is uneven due to learning abilities and resources. Students with disabilities present unique challenges to district performance, in that school accountability to federal Adequate Yearly Progress, is impacted by fixed proficiency levels. Alternatives to the traditional measure of competency in mathematics continue to impact how schools score on national and state indexes. The increased focus on performance assessment targets both individual and aggregate learning difficulties representative of the students those schools teach.

Innovation in the instrumental measurement of math criteria that will adequately capture abilities has improved how schools develop NCLBA curricula beyond standardized testing criteria. Canada"s national model of assessment, "Think Aloud" Protocol (TAPs) offers an alternative to its North American counterpart, through a combined approach to learning assessment incorporating informal methodologies (i.e., speech) and calibration of sequencing in student responses the test employs numbers – symbols with abstract and semantic meaning. Variance is factored into the facilitation of the approach. Memorization of those numerical sequences from pictograms with repetition in the audio transmission of the same inference to record response patterns. Number sequences are selected from the random number generator, illustrated in Figure 1.

Based on a simple associate memory test consisting of visual and auditory retention in sequences of seven (7) digits, the sequence is heard and read by students in correspondence with the test. The number series is then transferred to the test database, for retention of the sequences illustrated in Figure 2.

Number of Correct Answers

Visual Memory Test

Auditory Memory Test











Post interruption, a new number sequence is requested and recorded. Auditory assessment is done consecutively with each student and recorded for results to the test. Outcomes are calculated according to mean percentage according to the formula: C / N (100) = P, added to the total number of participants in each column. Once the division of the number of students with shared median scores is tallied, the total number of participants in the study multiplied by 100 to get the percentage. Aggregate distribution of the assessment is reflected in histogram; reporting on media memory in each test phase, as seen in the example where the Y-axis on the left side of the graph as a scale for the percentage of people from 0 to 100%, and on the bottom a scale for the number of correct responses from 0to7 in Figure 3.

Learning Tool: Math-Out-of-the-Box

A study of teacher facilitation of an innovative K-12 mathematics instructional tool Math-Out-of -the-Box, addresses the type of learning disability challenges seen in the two schools in the current study. Based on assessment testing respondent to stumbling blocks in standardized methodologies, the approach prompts quantitative thought through conceptual and problem-solving techniques. The Math-Out-of-the-Box Report examines the shift in student achievement in a 32 Title I school district in South Carolina between 2007 and 2008.

Outcomes of teacher implementation of the Math-Out-of-the-Box curriculum showed that students had gains in overall achievement, with proficiency and advanced levels increasing over other students at other Title 1 schools in the same district. Assessment by the teachers resulted in finding on learner-centered facilitation, and the potential of the instructional tool to exceed the performance of traditional approaches. The Report poses the following considerations pertinent to the current the school"s observed in the study through evaluation, shown in Table 1.

  1. Why did the fifth fifth-grades take longer to change?


  1. What will data show after a full implementation of Math Out of the Box?


  1. As more non-Title 1 schools adopt Math Out of the Box, how will student achievement in those schools be impacted?


  1. Are the differences indicated on the graphs significant?


  1. What components, if any, of the Math Out of the Box curriculum play, role in the transition from tradition to inquiry-based practices?


  1. Table 1. Math-Out-of-the-Box Criteria


Math-Out-of-the-Box methodology is designed to change how teachers facilitate instructional learning in mathematics. Both content and format are assessed and then put into instructional tasks with the objective of promoting performance in the classroom. Standardization is met through dimensional analysis of instructional practice, so that an iterative process supports average to above average fidelity in performance indexing. Five Dimensions of Instructional Practice in Math Out of the Box furthers those goals, with teacher training and follow-up survey informing "how often" students accomplish stated tasks according to a three point scale:

1) Number 1 – rarely or never seen behaviors;

2) Number 2 – often or sometimes seen behaviors;

3) Number 3 – regularly exhibited behaviors. The rating process is ongoing during instructional tasks in the Math Out of the Box curriculum.


In the 1960s, the modern "cognitive" approach to standardized testing evaluation of students in mathematics was established as official criteria in policy in the West. Psychological intervention became mandated curricula "function" in K-12 learning. From this point forward, individualized learning could only be sufficiently addressed through mathematical measurement. The emphasis on mathematics both in terms of learning assessment, and in terms of individual student performance has continued to be a challenge however, as the world of algorithmic thought extenuates rational abstraction beyond the scope of normative expectations. This is especially true where students face external or learning disability obstacles in their everyday use or even access to advanced instructional resources.

Standardization of "alternatives" then comprises much of contemporary education policy dialogue. Individualized education options such as Math-Out-of-the-Box are now more than ever sought in response to the need for more effective, universal applications in learning. If Jean Piaget (1969) once argued the early development models served as the foundation to constraints in cognitive development in children after the age of seven, then we truly are faced with a question of accountability issue if the first several years of K-12 education is already lost to resource restrictions and instructional incompetency.