Creative Education 2013. Vol.4, No.8, 521527 Published Online August 2013 in SciRes (http://www.scirp.org/journal/ce) http://dx.doi.org/10.4236/ce.2013.48076 Copyright © 2013 SciRes. 521 Tested In and Placed In: Are SixthGrade Boys and Girls Completing Early Challenge Math Coursework before They Are Ready? David C. Hemphill1, John W. Hill2 1Millard Public Schools, Omaha, USA 2Univertsity of Nebraska at Omaha, Omaha, USA Email: jhill@unomaha.edu Received June 9th, 2013; revised July 9th, 2013; accepted July 16th, 2013 Copyright © 2013 David C. Hemphill, John W. Hill. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The purpose of this study was to evaluate the algebra readiness outcomes of randomly selected sixth grade boys (n = 15) and girls (n = 15) who tested into and completed early challenge math coursework compared to the algebra readiness outcomes of randomly selected same school sixth grade boys (n = 15) and girls (n = 15) who tested below the admission threshold but were placed into and completed early challenge math coursework based on teachers’ recommendations to determine if these students, both tested in and placed in, were enrolled into higherlevel math courses before they were ready—a growing concern nationwide. Orleans Hanna Algebra Prognosis Test scores were analyzed using dependent t tests to determine sixthgrade pretestposttest within group progress and Orleans Hanna Algebra Prognosis Test scores were analyzed using Analysis of Covariance for between group statistical comparison across gender and placement conditions to determine rate of test score improvement. Between group challenge math end of sixthgrade report card grade scores were analyzed using Analysis of Variance, also across gender and placement conditions. Taken all together the study test scores and grade results clearly indi cate that boys and girls whether tested into or placed into sixthgrade challenge math coursework based on teacher recommendations were equally prepared and ready for seventhgrade prealgebra studies fol lowing a year of early challenge math. Finally, we assert that placement criteria and procedures will con tinue to predict student success where there are, in combination, a welldesigned rigorous math curricu lum, committed, caring, and skilled teachers, and motivated students—making early challenge math coursework placement the only appropriate option for students when these conditions are extant. Keywords: Algebra Readiness; Challenge Math; Sixth Grade Students; Tested In; Placed In Introduction Over the past two decades there has been a push to offer al gebra coursework earlier and earlier to all elementary and mid dle school students (Dulaney, 1996; Fensterwald, 2010; Steen, 1999). Currently, the goal of algebra for all mathematics policy in the United States is to provide early math experiences that will prepare students for the more formal study of algebra in high school (NCTM, 2000; Rivera, 2006). However, it is not clear what early algebra experiences should be and whether or not these early abstract math experiences will result in im proved advanced math achievement for all students (Knuth et al., 2005; Schmidt, 2004; US Department of Education, 2008). The push to have all middle school students complete math before they are ready has resulted in what Bracey (2008) has referred to as the great algebra hoax in California, where it has recently been determined that nearly 120,000 eighthgrade students, cur rently taking algebra, have math ability scores measured at the secondgrade level. Algebra, as recently as the 1990s, was con sidered a class for gifted math students. By 2007, 31% of all students in the eighthgrade nationally were taking algebra. The push for accelerated algebra courses in the middle school years is motivated, at least in part, by the results of the math scores of students in the United States compared to stu dents internationally on the Trends in International Mathemat ics and Science Study (TIMSS, 1999). In the TIMSS report United States students in the fourthgrade ranked 12th out of 26 nations, eighthgrade students ranked 28th out of 41 nations, and 12grade students ranked 19th out of 21 nations on the math examination covering content and cognitive dimensions. On the Program for International Student Assessment (PISA) test completed in 2006, United States 15yearold students’ average math score was lower than the Organization for Eco nomic Cooperation and Development (OECD) student average score. United States students averaged 474 and the OECD av erage was 498. This placed the United States students in the bottom quarter when compared with other participating nations (US Department of Education, 2010). Low scores on international measures often result in gov ernment mandates for sweeping reform in educational practices often dissociated from the realworld needs and abilities of students (Board, 2010; Guttenplan, 2010). Unfortunately, a stu
D. C. HEMPHILL, J. W. HILL dent who is misplaced in a more rigorous math class without the automatic basic skills need to complete and solve more complex problems may only learn failure (GreatSchools, 2010; Stacey, 2009). The National Assessment of Education Progress (NAEP) data suggests that the effort to push more kids into algebra math classes before students are ready is an unfortunate national trend. While lower achieving students only accounted for 8% of the students in higherlevel math classes in 2000 by 2005 the number taking higherlevel math courses rose to 28.6% (Lee, Grigg, & Dion, 2007; Loveless, 2008). California is leading the charge for algebra for all eighthgrade students. From 20032008, students taking algebra increased 63%. However, only 42% of those taking algebra scored proficient on the state algebra test. A study found that large numbers of eighthgrade students are retaking algebra in ninthgrade and doing worse the second time through the course (Fensterwald, 2010). Students who take algebra before they have a strong founda tion in basic math and have the mental development may find themselves unprepared for college or the work force. Students that are not prepared usually have to relearn math in a remedial class later which can hurt students chances for success when compared with students who are prepared for algebra and were enrolled in algebra when they were ready (GreatSchools, 2010; Steen, 1992; Steen, 1999). Review of Literature Algebra throughout the K12 Curriculum There is a real effort to include problem solving and mathe matical investigation into our students’ current challenge math curriculum (National Council of Teachers of Mathematics, 2002). This concerted effort to bolster our math curriculum, no doubt comes from reports such as the Program for International Student Assessment (PISA) as reported by the US Department of Education (2010). In the introduction of this document, data were given to show the United States poor performance when compared to other nations. A closer look at that data shows that PISA describes six mathematics literacy proficiency levels ranging from 1 to 6, the later being the most advanced. Twenty seven percent of US students scored at or above level 4 (above proficiency). This is lower than the other 32% of students in OECD countries on average that scored at or above level 4. According to the study level 4 students are able to complete higher order tasks like solving problems involving visual or spatial reasoning in unfamiliar contexts. While these results are not terrible, what is concerning is that nearly onequarter of United States students scored below level 2 indicating they are not able to consistently use basic computational skills to draw accurate conclusions regarding problems in reallife situations (US Department of Education, 2010). “Algebrafying” the K12 Curriculum Algebra has always acted as the gateway class to all higher level math courses (McCoy, 2005). However, for some, algebra is the reform gateway to K12 math curriculum for the next century. To some it is thought that the key to this algebra re form is integrating algebra across the K12 math curriculum (Katz, 2007; Kaput, 2000). Kaput (2000) refers to algebra in two ways; “algebra the institution” and “algebra the web of knowledge and skill” (p. 2). For many it is claimed that algebra for all is the charge of this institution. As Kaput states, “But this algebra is the disease for which it purports to be the cure!” It is this “algebra the web of knowledge and skill” that is needed in the math classrooms of today. When we think about including algebra into earlier and earlier grades, it is not the “algebra institution” we are referring too but the “algebra the web of knowledge and skill” in which we intend to transform mathematics curriculum (Kaput, 2000). In much of the research that falls into math or algebra curriculum reform we find less talk about the X’s and Y’s and more discussion of the connec tions, thought processes, and generalizations that can come from studying math concepts at a deeper level. Early algebra is an approach to educating students in the early grades that ex plore the deeper meanings of mathematics. It includes two foci: (1) generalizing, identifying, expressing, and justifying math structure, properties, and relationships and (2) reasoning and actions based on the forms of generalizations (Katz, 2007). According to many, early algebra is not a curriculum addition. It is not thought to be a separate list of activities or lessons that should be taught after the students have been taught math computation skills. As soon as students in elementary school are able to count and use math symbols, early algebra should be embedded in the math lessons being taught (VanNoy, 2010). It is also believed that early algebra is a way to bring depth of understanding to the mathematics understanding of young chil dren by digging deeper into the concepts being taught so that students can generalize relationships and properties of those concepts. Early algebra is not a “moving to earlier grade levels” of algebra skills that are usually taught in middle school as a prealgebra class. The goals of early algebra are for students to learn to reason algebraically as they begin to acquire the ideas behind symbolic algebraic language and explore math situa tions that draw on students’ mathematical knowledge in order to reflect, build arguments, and justify new ideas (Katz, 2007). Gender Issues and Mathematics There has been a great deal of research over gender differ ences in math abilities. Much research focuses on the under representation of women in the area of math and science (Else Quest, Hyde, & Linn, 2010; Halpern et al., 2007; Hyde, Fen nama, & Lamon, 1990; Penner, 2008; Valentine, 1998). Scores from the 2009 PISA show that 15yearold boys outperformed girl classmates by 20 points in overall math proficiency (NASSP 2011). However, when looking at the results of the National Assessment of Educational Progress over the last ten years, the reported gap between boys and girls is 2% (Geist & King, 2008). A closer look at NAEP data reveals that while girls do equally as well as boys and have made gains in math more recently, there is a difference in moderately complex pro cedures and reasoning for 13yearolds. Boys are more profi cient in this area, outperforming girls, 32.6% proficient to 25.6% proficient. When comparing 17yearolds, boys are 8.8% proficient on multistep problem solving and algebra compared to girls at 5.1% (James, 2007). Women have had great success in college. American women receive more college degrees than men every year, a trend that began in 1982, and continues to grow today. Even with these successes, females score significantly lower on many high stakes standardized tests, including the verbal and mathematics section of both the Scholastic Aptitude Test (SAT) and the Gra duate Record Examination (GRE) (Halpern et al., 2007). Copyright © 2013 SciRes. 522
D. C. HEMPHILL, J. W. HILL Females also score lower on mathematics tests that do not closely resemble the material that was taught in school, despite earning higher grades than males in school (Halpern, 2007; Willingham & Cole, 1997). In a metaanalysis study of gender differences in math per formance it was learned that there has been gender differences in math performance for years and that those differences are still with us today. Conclusions around the world tend to sug gest simply that males outscore females on math tests. A closer look at the research reveals that the difference is not visible in early childhood, but becomes more prevalent during adoles cents. It is thought that boys are better able to handle more complex problem solving and girls favor the less complex computation tasks (Hyde, Fennema, & Lamon, 1990). Biological and Social Factors in Early Mathematics Achievement In research there appear to be two themes that come to sur face as you look at gender difference in mathematics; biological and social factors. At first glance there may not appear to be much difference in the male and female brain, but a much closer look is needed to notice the difference between males and females. Through magnetic resonance imaging (MRI), scientist, have been able to learn a great deal about the differ ences of the brain between genders. The cerebral cortex is thicker on the right side in men and thicker on the left side in women. This indicates that the thicker side of the brain is more developed than the opposite side of the brain. The hemispheres of a female’s brain will appear to be more identical where a male’s brain is asymmetrical (Halpern, 2000). This difference means that a female will process spatial abilities in both hemi spheres while males use one hemisphere (Penner, 2008)—a fact evidenced in research of damaged brains by Gazzaniga, Ivry, & Magnum (as cited in Penner, 2008). Furthermore, males with damaged left hemispheres show a loss of verbal abilities and damaged right hemispheres experience a loss of spatial abilities. Females with damage to the left hemisphere see a decrease in spatial and verbal abilities but no apparent decrease is found with damage to the right hemisphere in females. Males have larger inferior parietal lobes so they are better at judging speed, estimating time, and rotating objects mentally. In fact, at very early ages, boys perform better than girls in this area, in many cases by close to a full standard deviation (Halpern, 2004). In a metaanalysis study of gender differences in math, data from the content domain of Space/Shape on the PISA, an area that measures understanding of spatial relationships, showed boys were slightly favored in this content area albeit with a low ef fect size of (d = 0.15; ElseQuest, Hyde, & Linn, 2010). However, girls are better at retrieving information from longterm memory and typically score better than boys on tests of verbal learning and the creation and understanding of com plex prose (Halpern, 2004). Male brains seem to be more spe cialized overall, whereas female brains seem to be more multi purpose. This brain difference is apparent in elementary school when math involves math facts, calculations, and the quick re trieval similar to that needed in language generation and under standing favor girls. In algebra, girls perform better on prob lems where the solution involves a process similar to those of language processing (Gallagher, Levin, & Cahalan, 2002; Hyde, Fennama, & Lamon, 1990). Another area of biological difference between males and fe males is the developmental process. Magnetic Resonance Im aging and Electro Encephalograph scans of male and female brains have given us images that show the brain of a 17year old boy are equivalent to the brain of an 11yearold girl. An other way of measuring brain maturation is to look at the de gree of myelination. Myelin, necessary for fast, clear nerve im pulse transmission, is a waxy material that coats the axons in the brain. An infant will have no myelin and by adulthood the brain will be full of the substance. Using this substance scientist show a three to four year gap in brain development between boys and girls. Males did not catch up to females until the age of 29 (Gallagher et al., 2002). We know that there are developmental difference in the brains and bodies of our children, but research is also trying to assess how much impact social factors play into the mathemat ics learning of our boys and girls. In July of 1992, a talking Barbie hit the shelves of stores and much to the public’s dismay uttered the phrase, “math class is tough.” According to Sax (2010) and Geist and King (2008) research shows that girls feel less confident in their ability to perform well on math tests while boys often show greater confidence or overconfidence in their abilities. Kloosterman, Tassell, Ponniah, and Essex (2008) found that most students, seventh through 12thgrade, believed that math is a genderneutral domain but female students were stronger in those beliefs than males. Boys who rated themselves as good or excellent in math felt more strongly that math is not a female domain. Another study showed that students’, when asked to nominate who is best in their class in language arts and math, named boys and girls equally in language arts, but in math the boys nominated only boys and the girls started nomi nating more boys than girls from the fourthgrade on (Räty, Kasanen, Kiiskinen, & Nykky, 2004). Social factors are also determined by parent influence. For example, in research by Leedy, LaLonde, and Runk in 2003 (as cited in Geist & King, 2008) parents of sons tend to expect their sons to learn math skills earlier than do parents of girls and as the children get older they expect their daughters to work hard to get good grades in math while parents of boys emphasize the learning of math. Regardless of the gender, higher levels of parental involvement with their children’s education equates to higher levels of performance in mathematics (Muller, 1998). According to a metaanalysis study by Lytton and Romney in 1991 (as cited by Halpern et al., 2007) there was no significant difference in how parents treated males and females in encour aging achievement but this study did not differentiate the dif ferent areas of study, for example language arts or mathematics. Furthermore, boys tend to gain more spatial experience because they tend to be allowed to roam over a greater area than girls who chose activities that are closer to home. This roaming of the neighborhood allows boys to have a better spatial under standing of the area as represented on drawings of maps be tween boys and girls (Halpern et al., 2007). This influence is an extension of the parent influence but is reinforced throughout the neighborhood as parents in the neighborhood allow boys more freedom to venture further from home. Admission Standards for Early Algebra Course Participation Understanding biological and social factors, math curriculum, and the readiness of students for taking algebra is important, but of equal importance is having an effective placement proc Copyright © 2013 SciRes. 523
D. C. HEMPHILL, J. W. HILL ess to enroll students into the correct math courses. The place ment process should help place a student on a path for mathe matics success throughout the middle school experience and into high school. Bracey (2008) and Loveless (2008) assert that algebra once was a class for gifted students but now has be come a class that all students must take, whether they are ready or not. For example in the research school district during the 20082009 school year 144 students, 43% of the total eighth grade population, were taking algebra as eighthgraders. There were also 19 seventhgrade students that were taking algebra during their seventhgrade year. In a check of enrollment num bers for algebra in 20052006, there were only 82 students tak ing algebra. This is a trend that appears to be growing in the research school as well as nationally. In this study the current method of selecting students into challenge math used a triangulated composite score based on the presixthgrade OrleansHanna test score, the fourthgrade Terra Nova math composite test score, and the school districts math Essential Learner Outcome (ELO) test score. These three scores are scaled to 15 points with each component sharing an equal part in the 15 points. Students with higher scores are placed in Challenge Math 6 and students below the cut score are recommended for Math 6 to prepare for more challenging math coursework in the seventhgrade. Students who scores are 35 or higher—up to 50 points—bypass the process of selection into challenge math and are placed in prealgebra for sixth grade. If students score less than 35 raw score points on the OrleansHanna, then the triangulation of scores is used. If a student is on the bubble between being placed in Math 6 or Challenge Math, the student’s fifthgrade teacher, is contacted by the middle school registrar in order to give his/her input on the best math placement. This recommendation involves the fifthgrade teacher making a decision for each student based on the knowledge that he/she was on the bubble for placement in Math 6 or Challenge Math 6. Fifthgrade teachers are not given detailed OrleansHanna scores to assist in their placement deci sions. Early Algebra Placement It appears that over the past two decades a growing trend of placing more and more students in algebra at earlier grades may be becoming the norm. This relatively new norm has potentially devastating consequences if not handled appropriately. Educa tors cannot take existing algebra curriculum and push it into lower grade levels and expect that all students will be success ful. As previously mentioned, algebra is a gateway course. A successful completion of algebra opens more opportunities for students. These students are able to complete more advanced coursework in mathematics and pursue the studies of more advanced careers such as, engineering and the medical field. Algebra for all is a noble educational goal, but it is not a realis tic goal when attempting to do so at the eighthgrade level. Not all students are ready for the abstract thinking involved in un derstanding algebraic concepts. However, government officials see algebra as the way to put the United States on top in the global assessment race. Parents see algebra as a rigorous course to push their child, while others see it as a key to a lucrative career (Steen, 1999). All educators need to ask some practical questions: First, Are all students ready for algebra? Secondly, is our mathematics curriculum getting students ready for algebra? And finally, what is the rush to get to algebra? The answers to these questions are the key to providing quality, student ready mathematics programs. Methodology Purpose of the Study The purpose of this study was to evaluate the algebra readi ness outcomes of randomly selected sixth grade boys and girls who tested into and completed early challenge math course work compared to the algebra readiness outcomes of randomly selected same school sixth grade boys and girls who tested below the admission threshold but were placed into and com pleted early challenge math coursework based on teachers’ recommendations to determine if these students, both tested in and placed in, were enrolled into higherlevel math courses before they were ready. Student Participant Demographics This study included a randomly selected group of students (n = 30) who met the measured test score criteria for challenge math placement and a randomly selected group of students (n = 30), who did not meet the measured test score criteria for chal lenge math placement but received challenge math based on fifthgrade teachers’ recommendations. These students were randomly selected from a total of 102 same school sixthgrade students with the same placement and gender conditions. Of the total number of selected subjects who met the measured test score criteria for challenge math placement (N = 60), 15 (50%) were boys and 15 (50%) were girls. Of the total number of selected subjects who did not meet the measured test score criteria for challenge math placement but received challenge math based on teacher recommendation 15 (50%) were boys and 15 (50%) were girls. Of the total number of selected sub jects who met the measured test score criteria for challenge math placement (n = 30) 30 (100%) were White. Of the total number of selected subjects who did not meet the measured test score criteria for challenge math placement but received chal lenge math based on teacher or parent recommendation (n = 30) 26 (86.6%) were White, 3 (10%) were Asian, 1 (3.3%) was AfricanAmerican. The age range for all study participants was from 10 years to 12 years. Math Achievement Dependent M easures The study analyzed math achievement as measured by stu dents’ pretest and posttest (a) Orleans Hanna Algebra Prognosis Test scores (Ciechalski, 2005; Daubert, 2006; Kuchemann & Secolsky, 1985; Toone, 2011) and (b) students’ final posttest challenge math report card grade scores. Implementation of the Independent Variables The independent variables for this study were sixthgrade boys and girls meeting measured test score criteria for chal lenge math placement compared to sixthgrade boys and girls not meeting measured test score criteria for challenge math placement but receiving challenge math placement based on teacher recommendation. These groups comprise the four re search arms of the study. All groups of students were randomly selected from the same student population and were in atten dance at the same research middle school throughout the study. Copyright © 2013 SciRes. 524
D. C. HEMPHILL, J. W. HILL Research Questions The following three research questions guided the study comparing within group and between group algebra prognosis test scores and between group challenge math report card grade scores for the gender and placement conditions. 1) Do sixthgrade Boys Tested In, or sixthgrade Girls Tested In, or sixthgrade Boys Placed In, or sixthgrade Girls Placed In lose, maintain, or improve their end of school year pretest fifth grade Orleans Hanna Algebra Prognosis test scores compared to their end of school year posttest sixthgrade Orleans Hanna Algebra Prognosis test scores? 2) Do sixthgrade Boys Tested In, or sixthgrade Girls Tested In, or sixthgrade Boys Placed In, or sixthgrade Girls Placed In have congruent or different posttest end of school year sixth grade rate of gain or loss Orleans Hanna Algebra Prognosis test scores? 3) Do sixthgrade Boys Tested In, or sixthgrade Girls Tested In, or sixthgrade Boys Placed In, or sixthgrade Girls Placed In have congruent or different posttest end of school year sixth grade final challenge math report card grade scores? Assumptions and Limitations of the Study The study has several strong features including: (a) district wide assessment process is used for placing students in middle school math classes, (b) the challenge math program is an es tablished and widely respected course option, (c) all subjects were enrolled in the same school district during the study and were in the same school within the district during the sixth grade year, (d) students placed in the challenge math class were taught the same district math curriculum, and (e) all students were assessed by the same standardized prognosis test. The exploratory study was confined to sixthgrade students (N = 60) participating in a yearlong challenge math course. The small number of study subjects could limit the utility and generaliza bility of the study results and findings. Permission from the appropriate school research personnel and University of Ne braska Medical Center/University of Nebraska at Omaha Joint Institutional Review Board for the Protection of Human Sub jects approval was granted for the study before data were col lected and analyzed. Results The first pretestposttest hypothesis was tested using the de pendent t test. Null hypotheses for OrleansHanna Algebra Prognosis Test score improvement over time were rejected for the end of fifthgrade pretest compared to ending sixthgrade posttest for all four groups where Boys Tested In, pretest M = 23.20, SD = 4.89, posttest M = 38.07, SD = 6.65; t(14) = 7.13, p < .001 (onetailed), ES = 1.867, Girls Tested In, pretest M = 21.20, SD = 4.81, posttest M = 36.33, SD = 9.96, t(14) = 9.87, p < .001 (onetailed), ES = 2.686, Boys Placed In, pretest M = 18.60, SD = 4.91, posttest M = 34.80, SD = 10.04, t(14) = 6.86, p < .001 (onetailed), ES = 2.010, and Girls Placed In, pretest M = 20.87, SD = 4.31, posttest M = 35.93, SD = 6.40, t(14) = 7.94, p < .001 (onetailed), ES = 2.099. The second posttestposttest hypothesis was tested using Analysis of Covariance (ANCOVA) with the pretest mean scores serving as the concomitant variable and the posttest scores as the dependent variable. The null hypothesis was not rejected for the posttest OrleansHanna Algebra Prognosis Test ANCOVA results between group comparison for Boys Tested In, (posttest M = 38.07, SD = 6.65; ANCOVA adjusted posttest M = 36.99), Girls Tested In (posttest M = 36.33, SD = 9.96; ANCOVA adjusted posttest M = 36.22), Boys Placed In (post test M = 34.80, SD = 10.04; ANCOVA adjusted posttest M = 35.93), and Girls Placed In (posttest M = 35.93, SD = 6.40; ANCOVA adjusted posttest M = 35.98), indicating rate of test score improvement equipoise for all placement and gender con ditions where (F(3, 55) = 0.06, p = .98). Because no significant main effect was found post hoc, contrast analyses were not con ducted. The third posttestposttest hypothesis was tested using Ana lysis of Variance (ANOVA). The null hypothesis was not re jected for the last trimester sixthgrade posttest challenge math course grade score posttestposttest ANOVA results be tween group comparison for Boys Tested In (M = 92.25, SD = 4.40), Girls Tested In (M = 93.75, SD = 4.52), Boys Placed In (M = 91.13, SD = 5.12) and Girls Placed In (M = 93.54, SD = 3.11), where (F(3, 56) = 1.18, p = .32). Because no significant main effect was found post hoc, contrast analyses were not con ducted. Conclusion Based on the results the following conclusions may be drawn from the study for each of the three research questions. Overall OrleansHanna Algebra Prognosis Test posttest com pared to pretest mean score change across gender and place ment conditions, all in the direction of statistically improved scores over time, validates gender and challenge math course work placement readiness for these students where Boys Tested In posttest OrleansHanna Algebra Prognosis Test score of 38.07 was +14.87 points greater than pretest, Girls Tested In posttest OrleansHanna Algebra Prognosis Test score of 36.33 was +15.13 points greater than pretest, Boys Placed In posttest OrleansHanna Algebra Prognosis Test score of 34.80 was +16.20 points greater than pretest, and Girls Placed In posttest OrleansHanna Algebra Prognosis Test score of 35.93 was +15.06 points greater than pretest. These scores represent an enviable pattern of math test score improvement across time from the end of the fifthgrade to the end of the sixthgrade for these students across gender and placement conditions. It is gratifying than that overall posttest compared to posttest ANCOVA results for ending sixthgrade OrleansHanna Alge bra Prognosis Test scores for sixthgrade boys meeting meas ured test score criteria for challenge math placement, sixth grade girls meeting measured test score criteria for challenge math placement, sixthgrade boys not meeting measured test score criteria for challenge math placement but placed into challenge math based on teacher recommendation, and sixth grade girls not meeting measured test score criteria for chal lenge math placement but placed into challenge math based on teacher recommendation were found to be congruent indicating rate of test score improvement equipoise across placement and gender conditions—again validating challenge math coursework placement readiness for these students. Moreover, mean post test OrleansHanna Algebra Prognosis Test scores across placement and gender conditions were measured just below or above the research school districts cut score of 35 required for automatic early placement into prealgebra classes where Boys Tested In posttest OrleansHanna Algebra Prognosis Test score of 38.07 was +3.07 points above the cut score, Girls Tested In Copyright © 2013 SciRes. 525
D. C. HEMPHILL, J. W. HILL posttest OrleansHanna Algebra Prognosis Test score of 36.33 was +1.33 points above the cut score, Boys Placed In posttest OrleansHanna Algebra Prognosis Test score of 34.80 was −0.20 points below the cut score, and Girls Placed In posttest OrleansHanna Algebra Prognosis Test score of 35.93 was +0.93 points above the cut score. Finally, converting the posttestposttest between group ana lysis of variance last trimester sixthgrade posttest challenge math classroom performance results into grade nomenclature helps put these students’ results in perspective where sixth grade boys meeting measured test score criteria for placement into challenge math mean score result of 92.25, was the equi valent of a grade of “B” or excellent math class performance, sixthgrade girls meeting measured test score criteria for place ment into challenge math mean score of 93.75, was the equiva lent of a grade of “A” or outstanding math class performance, sixthgrade boys not meeting measured test score criteria placed into challenge math based on teacher recommendation mean score of 91.13, was the equivalent of a grade of “B” or excel lent math class performance, and sixthgrade girls not meeting measured test score criteria placed into challenge math based on teacher recommendation mean score of 93.54, was the equivalent of a grade of a “A” or outstanding math class per formance. This overall excellent to outstanding classroom per formance is consistent with the significant within group posttest compared to pretest score improvement found in the first re search question and the rate of test score improvement equi poise noted in the second research question analysis. Further more, as with the second analysis no statistically significant variance was found between students regardless of placement and gender conditions. Taken all together the study test scores and grade results clearly indicate that whether tested in or placed in to challenge math coursework based on teacher re commendations these boys and girls were equally prepared and ready for seventhgrade prealgebra studies following a year of early challenge math. Discussion The practice used by the research school in testing and then placing students based on the results of these tests, and in some cases teacher recommendations, appears to be working effec tively based on the results of this study—that is boys and girls were not being placed into early challenge math coursework before they were ready. It should be noted that students who attended the research school and were participants in this study were mostly from higher socioeconomic homes with college educated parents who set high educational expectations for their children. Therefore, the study subjects were fortunate enough to have education role models in front of them each day and were being raised in what has been referred to as a concerted cultiva tion manner that implies focus on the importance of learning, education, achievement, and service to others based on learning success (Lareau, 2003). However, the research school district is a member of a two county, 11 school district learning commu nity required by state statute to provide education to students from families with fewer economic advantages. Studies show that students from families with fewer economic advantages perform less well than their peers from more socioeconomi cally advantaged homes (Baharudin & Luster, 1998; Jeynes, 2002; Eamon, 2005; Majoribanks, 1996; Hochschild, 2003; McNeal, 2001; Seyfried, 1998). Because the research school district will be enrolling increasing numbers of students from lower socioeconomic circumstances in response to the eco nomic diversity mandate of the aforementioned 11 school dis trict learning community legislation it will be important that the research school make every effort to place these students in Challenge Math 6 classes using both test results and teacher recommendations in consultation with the students parents. Final Thought Students that take challenge math in sixthgrade are on a math track for placement in prealgebra in seventhgrade and then placement in algebra in eighthgrade. While all groups in this study performed well during the sixthgrade year taking challenge math, it is not known how these students will perform throughout the remainder of their middle school and high school math studies. The premise of this study is that students are being pushed into higherlevel math courses before they are ready, therefore, additional research must be conducted to fol low these challenge math students who tested in to or were placed in to early challenge math coursework based on teacher recommendation in a longitudinal study to evaluate progress in later math courses. 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