Unfortunately, the traditional textbook-based skills approach focuses on memorizing by rote measurement facts (e.g., equivalent measures such as 12 inches = 1 foot) and measurement procedures (e.g., how to use a ruler)" (1998, p. 15-9).
Absent hands-on exercises, though, many young learners will not have an opportunity to construct an understanding of the process of measurement or a concept of measurement unit which can frequently result in mechanical and inappropriate applications of measurement knowledge and tools. For instance, Baroody and Coslick point out that many elementary-level children tend to confuse area with perimeter and vice versa; some common types of errors that are made by these young learners when using a ruler, for example, include the following:
Counting the number of has marks starting with 0 rather than the units between the marks;
Treating the 1 hashmark as the starting point instead of the 0 hashmark and counting the 2 hashmark as one; and,
Placing the edge of an object at the 1-inch hashmark rather than the 0 hashmark (Baroody & Coslick, 1998, p. 15-9).
Finally, these authors emphasize that, "Children should be encouraged to look for patterns and to use what they know to reinvent area and perimeter formulas. Deriving these formulas themselves can promote mathematical power in three ways: increase their confidence that they can make sense of mathematics, engage them in genuine mathematical thinking, and foster understanding" (Baroody & Coslick, 1998, p. 15-18). The rationale for using these exercises also relates to improving long-term retention and comprehension of these important measurement concepts: "Promoting adaptive expertise makes it less likely children will forget the formulas, more likely they can reconstruct them if they do, and far more likely they will be able to devise new formulas on their own" (Baroody & Coslick, 1998, p. 15-18).
The resources available for this exercise include the typical fifth-grade classroom materials available in Texas public schools, the TAKS Study Guides provide by the Texas Education Agency designed to help students strengthen the skills that are taught in class and tested on TAKS (the study guides are designed for students to use on their own or for students and families to work through together and concepts are presented in a variety of ways that will help students review the information and skills they need to be successful on the TAKS), as well as some inexpensive materials (i.e., pie pans, cardboard boxes, paper towel cardboard tubes, Frisbees, string, plastic tumblers, Styrofoam cups and so forth which were donated by the author).
The goal of this initiative speaks directly to the role of schools in providing young learners with the knowledge and skills they will need to succeed in school and in their professional careers. Therefore, based on the mandates established in Chapter 111. Texas Essential Knowledge and Skills for Mathematics, Subchapter a. Elementary (5.10): Measurement," the goal of this exercise is to provide fifth-grade public school students in the Texas primary school in question with a superior approach to learning the concepts of area, perimeter and volume and improve their performance on the state-mandated high-stakes testing regimens that are currently in place.
The Texas Education Agency (2007) provides the following student demographic categories used in Texas public schools.
Texas public school student demographics.
Economic Status student may be identified as economically disadvantaged by the district if he or she meets eligibility requirements for the federal free or reduced price lunch programs; Title II of the Job Training Partnership Act (JTPA); Food Stamp benefits; Temporary Assistance to Needy Families (TANF) or other public assistance; received a Pell grant or funds from other comparable state program of needs-based financial assistance; or, is from a family with an annual income at or below the official federal poverty line.
Districts assign student ethnicity from one of the following categories: American Indian or Alaskan Native (not evaluated separately for accountability); Asian or Pacific Islander (not evaluated...
Section 11302 and its subsequent amendments; or resided in the preceding school year or resides in the current school year in a residential placement facility in the district, including a detention facility, substance abuse treatment facility, emergency shelter, psychiatric hospital, halfway house, or foster group home.
Special Education Status
Special education status indicates the student is participating in a special education instructional and related services program or a general education program using special education support services, supplementary aids, or other special arrangements.
Source: Appendix D - Data sources, Texas Education Agency Accountability Manual, 2007, http://www.tea.state.tx.us/perfreport/account/2007/manual/app_d.html.
Relevant group characteristics
There are currently 29 pupils in the 5th-grade class in question; of these, 15 are male (51.72%) and 14 are female (48.27%); about three-quarters of the class (21 or 72.41%) are English-speaking pupils, with the remaining eight students (or 27.58%) being Spanish-speaking pupils.
Prior knowledge of topic
Many fifth grade pupils bring a good grasp of measurement concepts with them to school, but in some cases these concepts have been based on erroneous processes or are otherwise flawed in their rationale.
Entry level knowledge and skills
For the purposes of this exercise, all fifth-grade pupils will be assumed to possess the requisite knowledge and skills that are required to achieve promotion from the fourth grade.
Attitudes and/or motivation toward the subject
Attitudinal problems with learning mathematics can be confirmed by virtually any primary classroom teacher (Kenschaft, 1997). There are also some problems associated with the way math tests are designed. According to Hawkins and his colleagues (2005), many American fifth-grade pupils fail to achieve satisfactory results on mathematics tests because of the manner in which the tests are designed. These researchers report that many of these pupils react negatively to lengthy problems, a reaction that is compounded by the paucity of opportunities for success. To overcome these constraints, Hawkins and his colleagues recommend including some shorter math problems interspersed with the more difficult ones to maintain interest and commitment to succeed in these young learners. In this regard, Hawkins et al. (2005) suggests that a ratio of one-to-one is preferable: "The current results demonstrated that interspersing briefer, easier problems following each target problem (1:1 ratio) did increase target problem accuracy on written assignments" (p. 543).
According to Kenschaft…
Time broken into hours, days, weeks, and months must also be mastered. This is the grade level where statistics are introduced. Students learn to "Collect data using observations, surveys, and experiments and record appropriately," and then turn those observations into appropriate visual representations of them which would allow them to make predictions (4.S.2). The fifth grade set standards also aim to utilize previous points in order to get into more