Effects of using manipulative materials to teach remedial algebra to community college students on achievement and attitudes towards mathematics

This dissertation derived hypotheses from the theories of Piaget, Bruner and Dienes regarding the effects of using Algebra Tiles and other manipulative materials to teach remedial algebra to community college students. The dependent variables measured were achievement and attitude towards mathematics. The Piagetian cognitive level of the students in the study was measured and used as a concomitant factor in the study.^ The population for the study was comprised of remedial algebra students at a large urban community college. The sample for the study consisted of 253 students enrolled in 10 sections of remedial algebra at three of the six campuses of the college. Pretests included administration of an achievement pre-measure, Aiken's Mathematics Attitude Inventory (MAI), and the Group Assessment of Logical Thinking (GALT). Posttest measures included a course final exam and a second administration of the MAI.^ The results of the GALT test revealed that 161 students (63.6%) were concrete operational, 65 (25.7%) were transitional, and 27 (10.7%) were formal operational. For the purpose of analyzing the data, the transitional and formal operational students were grouped together.^ Univariate factorial analyses of covariance ($\alpha$ =.05) were performed on the posttest of achievement (covariate = achievement pretest) and the MAI posttest (covariate = MAI pretest). The factors used in the analysis were method of teaching (manipulative vs. traditional) and cognitive level (concrete operational vs. transitional/formal operational).^ The analyses for achievement revealed a significant difference in favor of the manipulatives groups in the computations by campus. Significant differences were not noted in the analysis by individual instructors.^ The results for attitude towards mathematics showed a significant difference in favor of the manipulatives groups for the college-wide analysis and for one campus. The analysis by individual instructor was not significant. In addition, the college-wide analysis was significant in favor of the transitional/formal operational stage of cognitive development. However, support for this conclusion was not obtained in the analyses by campus or individual instructor. ^

Effects of cooperative and individual integrated learning system on attitudes and achievement in mathematics

This study compares the effects of cooperative delivery (CD) and individual delivery (ID) of integrated learning system (ILS) instruction in mathematics on achievement, attitudes and behaviors in adult (16-21 yrs.) high school students (grades 9-13). The study was conducted in an urban adult high school in Miami-Dade County Public Schools using a pre-test/post-test design. Achievement was measured using the Test of Adult Basic Education (TABE) by CTB MC-Graw-Hill and Compass Learning. An attitudinal survey measured attitudes towards mathematics, the computer-related lessons, and attitudes toward group activities. Behavior was assessed using computer lab observations. ^ Two-way analyses of variance (ANOVA) were conducted on achievement (TABE and Compass) by group and time (pre and post). A one-way ANOVA was conducted on the overall attitude by group on the five components (i.e., content mathematics, delivery/computers, cooperative, partners, and self efficacy) and a one-way ANOVA was conducted on the on-task behavior by group. ^ The results of the study revealed that CD and ID students working on mathematics activities delivered by the ILS performed similarly on achievement tests of the TABE. The CD-ILS students had significantly better overall mathematics attitudes than the ID-ILS students and the ID-ILS group was on-task significantly more than the CD-ILS group. This study concludes that regularity and period of time over which the ILS is used may prove to be important variables although there were insufficient data to fully investigate the impact of models of use. Additionally, a minimum amount of time-on-system is necessary before gains can become apparent in innumeracy and increasing exposure to the system may have beneficial effects on learning. ^

Effects of Cooperative and Individual Integrated Learning System on Attitudes and Achievement in Mathematics

The purpose of this study was to determine the effects of a computer-based Integrated Learning Systems (ILS) model used with adult high school students engaging mathematics activities. This study examined achievement, attitudinal and behavior differences between students completing ILS activities in a traditional, individualized format compared to cooperative learning groups.

The Predictive Power of Homework Assignments on Student Achievement in Mathematics

This study examined the relationship between homework performance (percent of homework completed and percent of homework correct), student characteristics (Stanford Achievement Test score, gender, ethnicity, and socio-economic status), perceptions, and challenges and academic achievement determined by the students’ average score on weekly tests and their score on the Florida Comprehensive Assessment Test (FCAT) Norm Reference Test (NRT) mathematics assessment.

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

The impact of standards-based practices in mathematics on the achievement of low-performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

Investigating the influence of achievement on self-concept using an intra-class design and a comparison of the PASS and SDQ-1 self-concept tests

Background. The formation and measurement of self-concept were the foci of this research. Aims. The study aimed to investigate the influence of achievement on academic self-concept and to compare the Perception of Ability Scale for Students (PASS, Boersma & Chapman, 1992) with the Self-Description Questionnaire-1 (SDQ-1, Marsh, 1988). Sample. The participants were 479 grade 5 (mean age 126.6 months) coeducational Australian students, located in 18 schools. Method. An intra-class research design was used to investigate the influence of frame-of-reference on self-concept development. Results. As students' academic scores rose above their class mean their self-concepts increased and as students' academic scores fell below their class mean their self-concepts decreased. Students' difference from class mean predicted their self-concept scores. This finding was consistently shown across the reading, spelling, and mathematics domains using test and teaching rating data. A comparison between the PASS and the SDQ-1 demonstrated concurrent validity across self-concept domains. Conclusion. The findings support the notions that the social environment is a significant agent that influences self-concept, and that teacher ratings and standardised tests of achievement and the PASS and the SDQ-1 are valid measures for self-concept research.

Exploring the long-term associations between adolescents’ music training and academic achievement

There is a positive relationship between learning music and academic achievement, although doubts remain regarding the mechanisms underlying this association. This research analyses the academic performance of music and non-music students from seventh to ninth grade. The study controls for socioeconomic status, intelligence, motivation and prior academic achievement. Data were collected from 110 adolescents at two time points, once when the students were between 11 and 14 years old in the seventh grade, and again 3 years later. Our results show that music students perform better academically than non-music students in the seventh grade (Cohen’s d = 0.88) and in the ninth grade (Cohen’s d = 1.05). This difference is particularly evident in their scores in Portuguese language and natural science; the difference is somewhat weaker in history and geography scores, and is least pronounced in mathematics and English scores (η2 p from .09 to .21). A longitudinal analysis also revealed better academic performance by music students after controlling for prior academic achievement (η2 p = .07). Furthermore, controlling for intelligence, socioeconomic status and motivation did not eliminate the positive association between music learning from the seventh to the ninth grade and students’ academic achievement (η2 p = .06). During the period, music students maintained better and more consistent academic standing. We conclude that, after controlling for intelligence, socioeconomic status and motivation, music training is positively associated with academic achievement.

The effects of teaching a mathematics problem solving strategy on the problem solving ability of grade nine students

Forty grade 9 students were selected from a small rural board in southern Ontario. The students were in two classes and were treated as two groups. The treatment group received instruction in the Logical Numerical Problem Solving Strategy every day for 37 minutes over a 6 week period. The control group received instruction in problem solving without this strategy over the same time period. Then the control group received the treat~ent and the treatment group received the instruction without the strategy. Quite a large variance was found in the problem solving ability of students in grade 9. It was also found that the growth of the problem solving ability achievement of students could be measured using growth strands based upon the results of the pilot study. The analysis of the results of the study using t-tests and a MANOVA demonstrated that the teaching of the strategy did not significaritly (at p s 0.05) increase the problem solving achievement of the students. However, there was an encouraging trend seen in the data.

Correlation Among Math Anxiety, Attitudes Toward Math, and Math Achievement in Grade 9 Students: Relationships Across Gender

This research evaluated (a) the correlation between math anxiety, math attitudes, and achievement in math and (b) comparison among these variables in terms of gender among grade 9 students in a high school located in southern Ontario. Data were compiled from participant responses to the Attitudes Toward Math Inventory (ATMI) and the Math Anxiety Rating Scale for Adolescents (MARS-A), and achievement data were gathered from participants’ grade 9 academic math course marks and the EQAO Grade 9 Assessment of Mathematics. Nonparametric tests were conducted to determine whether there were relationships between the variables and to explore whether gender differences in anxiety, attitudes, and achievement existed for this sample. Results indicated that math anxiety was not related to math achievement but was a strong correlate of attitudes toward math. A strong positive relationship was found between math attitudes and achievement in math. Specifically, self-confidence in math, enjoyment of math, value of math, and motivation were all positive correlates of achievement in math. Also, results for gender comparisons were nonsignificant, indicating that gender differences in math anxiety, math attitudes, and math achievement scores were not prevalent in this group of grade 9 students. Therefore, attitudes toward math were considered to be a stronger predictor of performance than math anxiety or gender for this group.

Poisoning the mind: Arsenic contamination of drinking water wells and children's educational achievement in rural Bangladesh

Bangladesh has experienced the largest mass poisoning of a population in history owing to contamination of groundwater with naturally occurring inorganic arsenic. Prolonged drinking of such water risks development of diseases and therefore has implications for children's cognitive and psychological development. This study examines the effect of arsenic contamination of tubewells, the primary source of drinking water at home, on the learning outcome of school-going children in rural Bangladesh using recent nationally representative data on secondary school children. We unambiguously find a negative and statistically significant correlation between mathematics scores and arsenic-contaminated drinking tubewells at home, net of the child's socio-economic status, parental background and school specific unobserved correlates of learning. Similar correlations are found for an alternative measure of student achievement and subjective well-being (i.e. self-reported measure of life satisfaction), of the student. We conclude by discussing the policy implication of our findings in the context of the current debate over the adverse effect of arsenic poisoning on children.

Don’t aim too high for your kids: parental over-aspiration undermines students’ learning in mathematics

Previous research has suggested that parents’ aspirations for their children’s academic attainment can have a positive influence on children’s actual academic performance. Possible negative effects of parental over-aspiration, however, have found little attention in the psychological literature. Employing a dual-change score model with longitudinal data from a representative sample of German schoolchildren and their parents (N = 3,530; grades 5 to 10), we showed that parental aspiration and children’s mathematical achievement were linked by positive reciprocal relations over time. Importantly, we also found that parental aspiration that exceeded their expectation (i.e., over-aspiration) had negative reciprocal relations with children’s mathematical achievement. These results were fairly robust after controlling for a variety of demographic and cognitive variables such as children’s gender, age, intelligence, school type, and family SES. The results were also replicated with an independent sample of US parents and their children. These findings suggest that unrealistically high parental aspiration can be detrimental for children’s achievement.

Breaking the double-edged sword of effort/trying hard: developmental equilibrium and Longitudinal relations among effort, achievement, and academic self-concept

Ever since the classic research of Nicholls (1976) and others, effort has been recognized as a double-edged sword: whilst it might enhance achievement, it undermines academic self-concept (ASC). However, there has not been a thorough evaluation of the longitudinal reciprocal effects of effort, ASC and achievement,in the context of modern self-concept theory and statistical methodology. Nor have there been developmental equilibrium tests of whether these effects are consistent across the potentially volatile early-to-middle adolescence. Hence, focusing on mathematics, we evaluate reciprocal effects models over the first four years of secondary school, relating effort, achievement (test scores and school grades), ASC, and ASCxEffort interactions for a representative sample of 3,421 German students (Mn age = 11.75 years at Wave 1). ASC, effort and achievement were positively correlated at each wave, and there was a clear pattern of positive reciprocal positive effects among ASC, test scores and school grades—each contributing to the other, after controlling for the prior effects of all others. There was an asymmetrical pattern of effects for effort that is consistent with the double-edged sword premise: prior school grades had positive effects on subsequent effort, but prior effort had non-significant or negative effects on subsequent grades and ASC. However, on the basis of a synergistic application of new theory and methodology, we predicted and found a significant ASC-by-effort interaction, such that prior effort had more positive effects on subsequent ASC and school grades when prior ASC was high—thus providing a key to breaking the double-edged sword.

Precise Mathematical Language: Exploring the Relationship Between Student Vocabulary Understanding and Student Achievement

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, with teaching modeling and ample opportunities to use the language of mathematics, students’ understanding and use of specific mathematical vocabulary is increased.