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Alignment and Articulation

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Articulation and Alignment: Statistics in West Virginia Middle and High Schools The implementation of the 2002 No Child Left Behind Act establishes a necessity of every state to ensure that there is proper vertical alignment of curriculum in every subject (Clarke, Stow, Ruebling & Kayona, 2006; DuFour, DuFour, & Eaker, 2008). With a national push to align standards vertically, most states have worked toward creating and instating new standards. Clarke, et al. (2006) state the importance of standards is to give educators direction, focus, and accountability of the curriculum that they present in their classrooms. Organizations Selected

For the purpose of this analysis, the author has chosen to analyze the adjacent organizations of middle school, grades six through eight, and high school, grades nine through 12. The analysis focuses on the Next Generation Mathematics Content Standards and Objectives, as presented by the West Virginia Department of Education (2011). Because of the amount of standards presented, the analysis will be confined to a topic of the mathematics curriculum, statistics. The West Virginia Department of Education (2011) divides the mathematics standards for grades individually. Thus the author will be aggregating the sixth, seventh, and eighth grade curricular standards into a middle school category and aggregating the ninth, tenth, 11th, and 12th grade curricular standards into a high school category. Analysis of Curriculum Articulation and Alignment

There are apparent weaknesses with the statistics standards, including wording and alignment. The author divides these into two subheadings to discuss separately. Both of these weakness will be combined to articulate an improvement plan that when implemented could reduce or eliminate the weakness discussed in the next two sections.

Curriculum Articulation
In the analysis of the statistics standards there are two forms of alignment observed, horizontal and vertical. Horizontal alignment refers not only to the standards to be followed, but also the assessments used to determine the level at which the students understand the concepts presented by the standards (Case, 2008). The West Virginia Department of Education (2011) specifies that at the end of each year the students will be assessed according to the standards that the educators of that grade level are responsible for teaching. For example, the mathematics standards taught in a year would be assessed by a standardized test, which includes questions from each division of the standards, such as statistics. Vertical alignment differs as it the alignment of curriculum over the course of multiple years, such as how the content flows from the middle school to high school years (Case, 2008). The vertical alignment of the statistics standards established by the West Virginia Department of Education (2011) presents an issue to which student learning is negatively affected.

The middle school statistics standards illustrate that students must demonstrate the mastery of six different major concepts. The high school statistics standards illustrate that there are 10 topics in which the students must master. The differing concepts are correlating between the middle and high school as illustrated in Table 1.

Table 1.
Statistical Concepts Presented in the West Virginia Mathematics Standards

Middle School High School
1. Display data sets using a) dot plots, b) histograms, and c) box plots 1. Descriptive statistics, including: [remove colon (if the preceding words indicate a series follows, a colon is redundant)] a) dot plots, b) histograms, and c) box plots 2. Use measures of central tendency 2. Compare center and spread of two sets of data 3. Use measures of variability 3. Create and use two-way frequency tables 4. Determine the probability of the occurrence of an event 4. Use of scatterplots to display two sets of data 5. Probabilities of compound events using: a) tree diagrams, b) lists, c) tables, and d) simulations 5. Interpret linear models 6. Bivariate measurement data using: a) scatterplots and b) linear equations 6. Distinguish between relationships as correlation and causation 7. Apply independent and conditional probabilities

8. Compute probabilities of compound events
9. Draw inferences and conclusions from collected data 10. Interpret geometric probability concepts

In addition to displaying the standards mandated by the West Virginia Department of Education (2011), the author has used highlighting to illustrate the correlating statistics standards included at both the middle and high school. As illustrated, a majority of the middle school statistics standards are intertwined into the high school standards; however, they spread across varies years. For instance, the use of visual displays, such as dot plots, histograms, and box plots is taught within the sixth grade curriculum, and is not mandated to be reviewed until ninth grade (West Virginia Department of Education, 2011). This gap in time represents an issue that the author will address within the improvement plan.

Curriculum Alignment
Curriculum alignment should be a goal of every educational department as they seek to piece together standards across numerous grade levels (Wiles & Bondi, 2007). When there is apparent ambiguity within the standards, it stands that educators will have a difficult time with ensuring distinct curriculum alignment. As Wiles (2009) states, standards must be written by clearly stating the information to be measured as well as written in a form that leads to some form of assessment. Words used within the West Virginia Department of Education (2011) standards include understand, know, and observe, which do not condone a method of assessment to ensure that students achieve what the standards require.

Proper alignment requires that educators can rely on students mastering prior knowledge in previous years, thus preparing them to build upon that knowledge with new content. Without proper indicators, such as assessable standards, there is no way to ensure that students have that proper background knowledge to master the new materials (Clarke et al., 2006). The approach to teaching the same statistical concepts varies, depending on the grade level. For example, in sixth grade the development of visual displays of data will be fairly elementary; however, the displays expected from a ninth grade student build from that elementary understanding to a deeper level of comprehension. The language used within the standard presented by the West Virginia Department of Education (2011) specifies that the sixth grade student will understand visual displays and three years later students are to create the visual displays. There is a gap in which student understanding is not bridged from year to year to ensure complete comprehension (West Virginia Department of Education, 2011).

With several of the standards the West Virginia Department of Education (2011) specifies the existence of gaps in two distinct areas. The first area is the use of description in terms of center and spread. In the middle school mathematics classroom, students are expected to describe the spread and center of a set of data; take that knowledge base in the high school and be able to summarize the statistic characteristics (West Virginia Department of Education, 2011). Again the knowledge building block is evident in description of the implementation of linear models from the middle school to the high school. At the middle school level, the students are expected to place or create a linear function; taking “a more sophisticated look” as a high school student by analyzing the fit of the linear model to the two sets of data (West Virginia Department of Education, 2011, p. 70). Improvement Plan

The author’s improvement plan focuses on the unification of both the standards and the educators involved in using the curriculum in their classrooms. The dissection of the current statistics standards to demonstrate a concrete flow from middle school to high school as well as from grade to grade and will allow students to have not just a vast and thin level of understanding, but an in-depth comprehension of the statistical materials. By getting the educators together to assist in this process, the students benefit as the educators have an understanding of the mental capabilities of the students that they teach.

In addition to forming a flow within the curriculum, the improvement plan supports the writing of statistical standards to lead toward measurement. As Wiles (2009) states standards need to be measureable, thus allowing educators to determine the level of mastery achieved by educators. The use of Bloom’s Taxonomy will ensure that students are challenged according to the level in which they are at academically (Anderson, Krathwohl, & Bloom, 2001). Table 2 illustrates a logical advancement through a statistics standard. Table 2.

Logical Advancement through a Statistics Standard Using Bloom’s Taxonomy

Middle School High School
6th Grade 7th Grade 8th Grade 9th Grade 10th Grade 11th/12th Grade Students will record a set of data using a) dot plot, b) histogram, and c) box plot. Students will compare data using a) dot plot, b) histogram, and c) box plot. Students will construct a) dot plot, b) histogram, and c) box plot given data sets. Students will compare and contrast data using a) dot plot, b) histogram, and c) box plot. Students will collect data and compose interpretation using a) dot plot, b) histogram, and c) box plot. Students will interpret and justify display of data using a) dot plot, b) histogram, and c) box plot.

In addition to the logical advancement demonstrated through Table 2, the improvement plan will provide professional development for educators at all levels. This professional development offers methods of assessment at each level to ensure that students have progressed successfully through the appropriate level of taxonomy prior to moving on to the next grade level.

To align curriculum successfully, educators need to work together to benefit the students learning process. Although, West Virginia Department of Education (2011) presents several statistical standards that follow a concrete flow, this flow needs to be exhibited through all standards. The basis of improvement plan presented by the author is to connect the knowledge of the educators with the standards to determine the most effect flow as well as create standards that can be actively measured according to Bloom’s Taxonomy. Students’ need a solid movement through Bloom’s Taxonomy to ensure that there is complete comprehension and understanding of the statistical concepts presented through the middle school and high school (Anderson, Krathwohl, & Bloom, 2001). As DuFour, DuFour, and Eaker (2008) the standards and assessments are given to the benefit of the student, with the plan to promote a greater success rate with students in the area of statistics.


Anderson, L. W., Krathwohl, D. R., & Bloom, B. S. (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. London: Longman. Case, B. (2008). Horizontal and vertical alignment. Pearson Education. Clarke, N. A., Stow, S., Ruebling, C. & Kayona, F. (2006). Developing standards-based curricula and assessments: Lessons learned from the field. The Clearing House, 79(6), 258-261. * DuFour, R., DuFour, R., & Eaker, R. (2008). Revisiting professional learning communities at work: New insights for improving schools. Bloomington, IN: Solution Tree Press. * West Virginia Department of Education. (2011). Next generation content standards and objects for mathematics in West Virginia schools (Report No. 2520.2B). Charleston, WV: West Virginia Board of Education. * Wiles, J. & Bondi, J. (2007). Curriculum development. (7th Ed.). Columbus, OH: Merrill. * Wiles, J. (2009). Developing successful K-8 schools: A principal’s guide. Thousand Oaks, CA: Corwin Press.

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