An analysis of the distribution and use of teaching aids in mathematics in selected Windhoek secondary schools

This study investigates the types of mathematics teaching aids available at both public and private secondary schools in Windhoek. The study characterises their usage and source as well as teachers’ perceptions towards the use of such teaching resources in the Mathematics classroom. The study is grounded in an interpretive paradigm and employed a mixed methods approach to generate both quantitative and qualitative data in two sequential phases. Phase 1 of the research process, which involved 75 Mathematics teachers, took the form of an audit of the availability and use of teaching aids at 25 secondary schools in Windhoek. A case study methodology was adopted in Phase 2 which focused on five purposively selected schools that displayed different characteristics in terms of the availability of teaching resources. The study found that the majority of teachers at secondary schools in Windhoek have a positive attitude towards the importance and role of teaching aids in Mathematics, seeing them as promoters of hands-on engagement, visual reasoning, active participation and motivation amongst learners. However, in some instances schools are underresourced with respect to certain types of teaching aids, specifically graph boards, geoboards, geometric models and computers. A need for appropriate in-school support on the use of teaching aids was also identifie

Teachers\u27 Perceptions of Manipulatives During Middle School Math Instruction

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district\u27s math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers\u27 perceptions of PD and perceived self-efficacy regading the implementation of manipulatives. Knowles\u27s andragogy and Piaget\u27s cognitive development theories framed this study. A homogeneous sample of 12 voluntary participants with more than 5 years teaching middle school math, both with and without access to manipulatives, volunteered to participate in this study. Data from observations, interviews, and archival documents were analyzed using comparative and inductive analyses and were analytically coded. Participants reported a need for PD that focused on physical and virtual manipulatives (PM and VM) and a low perceived self-efficacy regarding manipulatives use during math instruction. A blended PD using face-to-face and distance learning formats was designed to increase math teachers\u27 knowledge of and perceived self-efficacy with PM and VM for math instruction. This endeavor may contribute to positive social change by reforming PD opportunities to support teachers\u27 practice and self-efficacy using manipulatives during math instruction, ultimately increasing student performance

Using virtual manipulatives for 10-frame lessons with primary students: an in-depth educational study

This mixed methodology case study focused on the use of virtual manipulatives and technology in Grade 1 and Grade 2 number sense. This descriptive study examined the effectiveness of applet 10-frame lessons by comparing their use to other models. Data were collected from interviews, transcripts, checklists, and journal entries. Information revealed the number of times models were used and on students' attitudes and behaviours while using them. Student behaviours included time on task, repeated practice, the number of times students needed help, and how long it took to complete the tasks. Academic growths were measured using pre- and post-assessments and performance tasks rubrics. Students' attitudes towards the use of technology, specifically netbooks and an interactive whiteboard were analyzed and presented. The results of this study suggest that the applet models can be as effective as their concrete counterparts, and the students in this study enjoyed using technology while learning mathematics. --Leaf ii.The original print copy of this thesis may be available here: http://wizard.unbc.ca/record=b186283

The effectiveness of using manipulatives to teach fractions

The current study will focus on the effectiveness of using manipulatives when teaching fractions to elementary school students. Learning the concepts of fractions can be one of the most difficult skills to master for elementary level students. With so many different ways to expose students to manipulatives and enhance their fraction learning experience, it is important to examine how effective these teaching tools can be with respect to student achievement. The current study will discuss the effectiveness on student achievement when manipulatives are used during the teaching process. The main focus will be on student growth after being taught concepts of fractions including addition and subtraction while using manipulatives to engage them in their lessons. The students involved in this study are in one fourth grade class. This class includes 18 students that are performing at various achievement levels. Some of the participants have specific learning disabilities which hinder their ability to retain mathematical concepts without repetition over a longer period of time. The lessons being taught are included in the Everyday Mathematics fourth grade curriculum for fraction concepts. This curriculum is the Vineland Public Schools district wide mathematics curriculum. The teachers are responsible for teaching this curriculum using manipulatives for specific lessons. The study is taking place of a time span of four weeks. They will be tested prior to being taught the unit on fractions. They will be divided into two groups: one group will be instructed using integration of manipulatives and the other group will be instructed using worksheets and direct instruction including teacher modeling. Both groups will be given a post test to determine if the use of manipulatives was effective. This study will consist of comparing students\u27 assessment scores when being taught the concepts of fractions while using manipulatives and students\u27 assessment scores when they are taught without the use of manipulatives. An independent sample T-test revealed that students working with manipulatives during instructional time, small group time, and independent tasks demonstrated a significant amount of growth as compared to their peers that did not use manipulatives during any time of the learning process

SOLVING LINEAR EQUATIONS: A COMPARISON OF CONCRETE AND VIRTUAL MANIPULATIVES IN MIDDLE SCHOOL MATHEMATICS

The purpose of this embedded quasi-experimental mixed methods research was to use solving simple linear equations as the lens for looking at the effectiveness of concrete and virtual manipulatives as compared to a control group using learning methods without manipulatives. Further, the researcher wanted to investigate unique benefits and drawbacks associated with each manipulative. Qualitative research methods such as observation, teacher interviews, and student focus group interviews were employed. Quantitative data analysis techniques were used to analyze pretest and posttest data of middle school students (n=76). ANCOVA, analysis of covariance, uncovered statistically significant differences in favor of the control group. Differences in posttest scores, triangulated with qualitative data, suggested that concrete and virtual manipulatives require more classroom time because of administrative issues and because of time needed to learn how to operate the manipulative in addition to necessary time to learn mathematics content. Teachers must allow students enough time to develop conceptual understanding linking the manipulatives to the mathematics represented. Additionally, a discussion of unique benefits and drawbacks of each manipulative sheds light on the use of manipulatives in middle school mathematics

Effects of the use of manipulative materials on grade nine learners’ performance in fractions in public high schools in Chris Hani West Education District, South Africa

The purpose of this study was to investigate the effects of the use of manipulative concrete materials on grade 9 learners’ performance in fractions in public high schools in Chris Hani west education district, in the Eastern Cape Province of the Republic of South Africa. Two hundred and fifty (250) grade nine (9) learners, whose ages ranged between 13-16 years, and ten (10) educators teaching grade nine mathematics, were selected from 40 public high schools with the use of stratified, systematic random sampling, convenience and purposive sampling methods. One hundred and twenty-five (125) learners were put into the experimental group, and another one hundred and twenty-five (125) learners were put into a control group through systematic random sampling method. Pre-test, Post-test, and Control group quasi-experimental design were used as research designs to collect data. Two research instruments were developed. These included: A Fractions Achievement Test (FAT), and Students Questionnaire on Manipulative Concrete Materials (SQMCM). The experimental group were taught with the Manipulative Concrete Materials (Cuisenaire rods, Fraction bar/Fraction title, Paper folding and Computer assisted manipulative), whilst the control group was taught through the lecture method. Four (4) null hypotheses were generated and tested at 0.05 level of significance. The data collected were analysed using Analysis of Covariance (ANCOVA) to find the Mean, Standard Deviation and t-test. The mean and standard deviation were used to compare the pre-test and post-test results between the Experimental group and the Control group. The analysed results of the means, standard deviations and t-tests were used to reject the null hypotheses. The analysed results were illustrated as followed: Cuisenaire rods pre-test (mean = 8.372, SD=1.770), post-test (mean = 12,428, SD=4.732), t=13,024 p< 0.05. Hypothesis (H01) was rejected : Fraction tiles/fraction bars pre-test (mean = 8.372, SD=1.770), post-test (mean = 11,42, SD=3.67), t=12,10 p< 0.05. Hypothesis (H02) was rejected : Paper folding pre-test (mean = 8.372, SD=1.770), post-test (mean = 11,792, SD=4.256), t=12,024 p< 0.05. Hypothesis (H03) was rejected : Computer assisted manipulative pre-test (mean = 8.372, SD=1.770), post-test (mean = 12,212, SD=4.569), t=12,801 p< 0.05. Hypothesis (H04) was also rejected. The comparison of the mean scores and iv standard deviation between the Experimental groups and Control groups indicated that there was no significant difference in the Pre-test in all cases. On the other hand, the mean scores and standard deviations between the Experimental group and Control group in the Post-test showed a vast difference in all cases. There were improvement in the mean scores, and slightly difference in the standard deviations in the Experimental groups, whilst there were drops in the mean scores and standard deviations of the Control groups in all cases. From the studies, there was an indication that manipulative concrete materials have significant effects on grade nine learner’s performance in fractions. It was therefore suggested that manipulative concrete materials should be incorporated into the instructions of fractions in mathematics.Thesis (PhD) -- Faculty of Education, 202

Effects of the use of manipulative materials on grade nine learners’ performance in fractions in public high schools in Chris Hani West Education District, South Africa

The purpose of this study was to investigate the effects of the use of manipulative concrete materials on grade 9 learners’ performance in fractions in public high schools in Chris Hani west education district, in the Eastern Cape Province of the Republic of South Africa. Two hundred and fifty (250) grade nine (9) learners, whose ages ranged between 13-16 years, and ten (10) educators teaching grade nine mathematics, were selected from 40 public high schools with the use of stratified, systematic random sampling, convenience and purposive sampling methods. One hundred and twenty-five (125) learners were put into the experimental group, and another one hundred and twenty-five (125) learners were put into a control group through systematic random sampling method. Pre-test, Post-test, and Control group quasi-experimental design were used as research designs to collect data. Two research instruments were developed. These included: A Fractions Achievement Test (FAT), and Students Questionnaire on Manipulative Concrete Materials (SQMCM). The experimental group were taught with the Manipulative Concrete Materials (Cuisenaire rods, Fraction bar/Fraction title, Paper folding and Computer assisted manipulative), whilst the control group was taught through the lecture method. Four (4) null hypotheses were generated and tested at 0.05 level of significance. The data collected were analysed using Analysis of Covariance (ANCOVA) to find the Mean, Standard Deviation and t-test. The mean and standard deviation were used to compare the pre-test and post-test results between the Experimental group and the Control group. The analysed results of the means, standard deviations and t-tests were used to reject the null hypotheses. The analysed results were illustrated as followed: Cuisenaire rods pre-test (mean = 8.372, SD=1.770), post-test (mean = 12,428, SD=4.732), t=13,024 p< 0.05. Hypothesis (H01) was rejected : Fraction tiles/fraction bars pre-test (mean = 8.372, SD=1.770), post-test (mean = 11,42, SD=3.67), t=12,10 p< 0.05. Hypothesis (H02) was rejected : Paper folding pre-test (mean = 8.372, SD=1.770), post-test (mean = 11,792, SD=4.256), t=12,024 p< 0.05. Hypothesis (H03) was rejected : Computer assisted manipulative pre-test (mean = 8.372, SD=1.770), post-test (mean = 12,212, SD=4.569), t=12,801 p< 0.05. Hypothesis (H04) was also rejected. The comparison of the mean scores and iv standard deviation between the Experimental groups and Control groups indicated that there was no significant difference in the Pre-test in all cases. On the other hand, the mean scores and standard deviations between the Experimental group and Control group in the Post-test showed a vast difference in all cases. There were improvement in the mean scores, and slightly difference in the standard deviations in the Experimental groups, whilst there were drops in the mean scores and standard deviations of the Control groups in all cases. From the studies, there was an indication that manipulative concrete materials have significant effects on grade nine learner’s performance in fractions. It was therefore suggested that manipulative concrete materials should be incorporated into the instructions of fractions in mathematics.Thesis (PhD) -- Faculty of Education, 202