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Academic Achievement Outcomes: A Comparison of Montessori and Non-Montessori Public Elementary School Students

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... En ce qui concerne les compétences en lecture, six études ont trouvé de meilleures performances chez les élèves Montessori que chez les élèves en classes conventionnelles en maternelle (Lillard & Else-Quest, 2006; Lillard, 2012) et en élémentaire (Brown & Lewis, 2017;Mallett & Schroeder, 2015;Manner, 2007;Rodriguez et al., 2003) alors que deux études ont trouvé des performances similaires entre les deux groupes en élémentaire (Lillard & Else-Quest, 2006;Mallett & Schroeder, 2015). ...
... En ce qui concerne les compétences en lecture, six études ont trouvé de meilleures performances chez les élèves Montessori que chez les élèves en classes conventionnelles en maternelle (Lillard & Else-Quest, 2006; Lillard, 2012) et en élémentaire (Brown & Lewis, 2017;Mallett & Schroeder, 2015;Manner, 2007;Rodriguez et al., 2003) alors que deux études ont trouvé des performances similaires entre les deux groupes en élémentaire (Lillard & Else-Quest, 2006;Mallett & Schroeder, 2015). ...
... D'après la revue de la littérature que nous avons réalisée dans le chapitre 3, les résultats des études menées précédemment rendent la génération d'hypothèses claires difficile concernant les résultats attendus en mathématiques. En effet, des études ont trouvé de meilleures performances chez les élèves Montessori que chez les élèves en classes conventionnelles en maternelle (Chisnall & Maher, 2007;Laski, Vasilyeva, & Schiffman, 2016;Lillard & Else-Quest, 2006), en élémentaire (Mallett & Schroeder, 2015;Mix et al., 2017;Peng & Md-Yunus, 2014;Reed, 2008) et au lycée ( Dohrmann et al., 2007). Cependant, des études ont également trouvé des performances similaires chez les élèves Montessori et chez les élèves en classes conventionnelles en maternelle (Chisnall & Maher, 2007;Lillard, 2012;Mix et al., 2017), en élémentaire (Brown & Lewis, 2017;Laski et al., 2016;A. ...
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La pédagogie Montessori est une méthode d’éducation qui a été mise au point au début du siècle dernier par Maria Montessori pour des enfants d’un quartier défavorisé de Rome en Italie. Depuis sa création, elle s’est développée à la marge de l’éducation nationale et se retrouve principalement dans des écoles privées. La pédagogie Montessori devient cependant de plus en plus populaire auprès des enseignants de l’école maternelle publique. Ce récent engouement apparaît fondé à la vue de plusieurs principes de cette méthode. En effet, elle promeut l’autonomie, l’auto-régulation, la coopération entre pairs d’âges variés et l’apprentissage à partir de matériels sensoriels et auto-correctifs. Ces caractéristiques sont plutôt en accord avec les connaissances scientifiques sur l’apprentissage et le développement de l’enfant. Cependant, à ce jour, les preuves expérimentales rigoureuses de son efficacité sont limitées. Dans cette thèse, nous avons mesuré les compétences langagières, mathématiques, exécutives et sociales d’enfants d’une école maternelle, repartis aléatoirement entre des classes appliquant la pédagogie Montessori ou une pédagogie conventionnelle. Nous avons suivi leurs progrès au cours des trois années de l’école maternelle (étude longitudinale) et avons comparé les performances des enfants en fin de Grande Section (étude transversale). Nous avons également élaboré une mesure pour évaluer objectivement la qualité d’implémentation de la pédagogie Montessori dans cette école, situé dans un quartier défavorisé. Nos résultats ne montrent pas de différences entre les groupes dans les domaines des mathématiques, des compétences exécutives et des compétences sociales. Cependant, les enfants issus des classes Montessori avaient de meilleures performances en lecture que les enfants issus des classes conventionnelles en fin de Grande Section. La pédagogie Montessori apparaît donc comme adaptée à l’apprentissage de la lecture chez le jeune enfant
... Montessori education became widespread in mainland China in the late 1990s and 2000s (Shi, 2012(Shi, , 2015, yet little is known about classroom implementation practices. Evaluating implementation practices is relevant and meaningful as international research confirms Montessori preschool programs that are high in implementation fidelity result in better outcomes for children not only academically but also in areas of executive function, social development, motivation, and others (Diamond, 2013;Diamond and Lee, 2011;Ervin et al., 2010;Lillard, 2012;Lillard and Else-Quest, 2006;Lillard et al., 2017;Mallett and Schroeder, 2015;Rathunde and Csizszentmihaly, 2005). This study surveyed 210 in-service Montessori teachers in China to explore implementation practices of Montessori teachers in mainland China. ...
... Localization is a valid concern to ensure the suitability of Montessori education yet at the same time, localization insinuates a change from the original model. This becomes an issue of concern as it is broadly agreed upon by Montessori research that Montessori education that adheres to practices as outlined by Montessori in her writings results in better outcomes for children (Diamond, 2013;Diamond and Lee, 2011;Ervin et al., 2010;Lillard, 2012;Lillard and Else-Quest, 2006;Lillard et al., 2017;Mallett and Schroeder, 2015;Rathunde and Csizszentmihaly, 2005). The term used to describe this adherence to fundamental Montessori practices is implementation fidelity (O'Donnell, 2008), and while there is not yet a reliable instrument for measuring the fidelity of a Montessori program (Murray et al., 2017), there are agreed-upon guidelines and standards based on Montessori's writings as to what constitutes a high-fidelity Montessori program (AMIUSA, 2020;Lillard, 2012;Lillard and Heise, 2016;Lillard and McHugh, 2019a, 2019b, NCMPS, 2016. ...
... The literature review will discuss the theory and research surrounding four primary Montessori practices alongside the existing literature on how such practices have been adapted in Chinese Montessori classrooms due to localization pressures. 2013; Diamond and Lee, 2011;Ervin et al., 2010;Lillard, 2012;Lillard and Else-Quest, 2006;Lillard et al., 2017;Mallett and Schroeder, 2015;Rathunde and Csizszentmihaly, 2005). According to the National Center for Montessori in the Public Sector (NCMPS), exemplary Montessori practices that represent a highfidelity Montessori program include mixed-aged classrooms based on Montessori's theory of human development, classrooms managed and run by a single, trained head teacher accompanied by a non-teaching classroom assistant, a classroom composed of "no fewer than 24 students supervised by two adults", and a three-hour uninterrupted morning work cycle and a two-hour afternoon work cycle for older children (NCMPS, 2016). ...
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This descriptive research work highlights the implementation practices of Montessori education in mainland China and the concerns over Montessori education’s localization in mainland China. Localization can be understood as the adaptive process Montessori education undergoes in order to fit within Chinese culture. Two hundred and ten in-service Montessori teachers and administrators in China were surveyed to discover information concerning implementation practices in the following areas: mixed-aged classrooms, whether classrooms were co-teaching, student-to-teacher ratios, and morning and afternoon work cycles. The study found that the majority of classrooms were mixed-aged, reflecting high-fidelity Montessori practices. However, it also found that classrooms are co-teaching, have lower student–teacher ratios, and shortened work cycles, reflecting a departure from high-fidelity Montessori implementation. While localization should be considered to safeguard Montessori education’s sustainability, Chinese Montessori educators should also reflect on these findings as high implementation fidelity has been linked to better student outcomes.
... Indeed, findings from other studies indicate that a Montessori foundation at preschool may be important for optimal math learning outcomes at higher ages. Mallett and Schroeder (2015) assessed achievement differences from first through fifth grade for Montessori and non-Montessori school students in Dallas public schools using the Iowa Test of Basic Skills (ITBS) in grades 1 and 2, and the Texas Assessment of Knowledge and Skills (TAKS) in grades 3 through 5. No significant difference was found between groups in first through third grades, but emerged in favour of Montessori in fourth and fifth grades. ...
... The higher scores from the STEM-focused magnet may have elevated the magnet school scores to be on par with the Montessori schools, but this is difficult to ascertain due to limited information on comparison schools. Like the students in Mallett and Schroeder's (2015) study, the Montessori Elementary students may not have been in Montessori preschools. Laski, Vasilyeva, and Schiffman (2016) present an alternative possibility: that Primary Montessori programmes, but not Elementary Montessori programmes, confer math advantages. ...
... Secondly, high-fidelity Montessori schools are likely to confer advantages in math relative to conventional schools (e.g. Lillard & Else-Quest, 2006;Mix et al., 2017;Dohrmann et al., 2007;Lillard et al., 2017;Mallett & Schroeder, 2015). Studies featuring Montessori schools with discernibly lower fidelity (Ansari & Winsler, 2014Brown & Lewis, 2017;Miller & Bizzell, 1983, 1984Peng & Md-Yunus, 2014), or reporting little programme information (Laski et al., 2016;Lopata et al., 2005) have usually simply not found a difference. ...
Article
The math curriculum of the Montessori system of education for children ages 3–12 is distinctive, incorporating multiple manipulatives and educational practices which have theoretical and empirical support in research. However, studies investigating the math achievement and learning of Montessori students and alumni have not consistently found Montessori programmes to be more effective than conventional or other programmes. Through a detailed review of such studies, we find that a Montessori advantage in math is more likely when programmes adhere to important principles of Montessori education, when students have had longer immersion in Montessori programmes, and when assessments are more conceptual in nature. We suggest that future research should take into account programme fidelity and enrolment duration, and outline other directions for future research.
... Using standardized scores for math and ELA, researchers found worse results in ELA for Montessori in 8 th grade but no difference in math, nor in either subject in 4 th grade (Lopata et al., 2005). Another study compared more than 500 students in two public Montessori schools to a similar number of students in other demographically comparable public schools in the same district (Mallett & Schroeder, 2015). No significant differences were found in reading or math in first, second, or third grades, suggesting the samples were equal at the outset. ...
... The finding that Montessori schools had higher ELA scores in every comparison in this study aligns with prior research showing that Montessori students do well in ELA. Although results in some other studies could also reflect selection (Brown & Lewis, 2017;Culclasure et al., 2018;Mallett & Schroeder, 2015), this is not the case for studies that used random lotteries, and thus selection was controlled for (Courtier et al., 2021;Lillard & Else-Quest, 2006;Lillard et al., 2017); in one of these, low-income Montessori students improved more in reading across preschool than controls even though their Montessori teachers had no formal Montessori training (Courtier et al., 2021). The method with which reading is taught in Montessori is well-supported by other research, which could explain these findings. ...
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Although Montessori is the most common unconventional education model, no multi-state study has compared standardized test proficiency of Montessori schools with districts. Here we report on this for the 10 states/regions with the most public Montessori schools (n = 195). In 3rd grade, Montessori schools were less proficient in math but more proficient in ELA. In 8th grade they were also more proficient on ELA and showed a trend to greater proficiency in math. Black, Hispanic, and economically disadvantaged students at Montessori schools were more proficient on ELA tests, and performed better or similarly on math tests, at both grade levels. Achievement gaps were generally smaller. Difference in percent proficient in 8th grade controlling for 3rd grade was consistently greater at Montessori schools than in districts. Potential reasons for the different performance of Montessori schools are discussed.
... Mathematics and language arts −Simple comparison study −Parents selected school enrollment +Partial low-income sample Mallett and Schroeder (2015) Grades 1 to 5 Reading and mathematics −Simple comparison study −Parents selected school enrollment +Partial low-income sample Rule and Stewart (2002) Kindergarten Fine motor skills −Simple comparison study −Parents selected school enrollment −Teachers chose treatment or control +Partial low-income sample D. J. Ackerman ...
... A sixth study (Mallett & Schroeder, 2015) was situated in a single public school district in Texas and examined the 2011 standardized reading and math test scores of 1,035 Grades 1-5 Montessori (n = 518) and non-Montessori (n = 517) students. Forty-two percent of the sample was low income, but the Montessori students had to apply for admission. ...
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The Day 1 Academies Fund aims to support a network of high‐quality, full‐scholarship, Montessori‐inspired preschools in underserved communities. To provide insight into the fund's pedagogical inspiration, in this report I provide a high‐level overview of the Montessori preschool landscape in the United States. This overview includes 5 key programmatic elements of a traditional Montessori approach to teaching and learning in classrooms serving preschool‐aged children, the reported availability of Montessori programs that enroll 3‐ and 4‐year‐old children, and what is known about enrollees' demographics. To situate this information in the larger, publicly financed, early education policy context, I also provide similar data for state‐funded pre‐K and federally funded Head Start programs for preschoolers. In addition, I review research on children's outcomes after participating in U.S.‐based Montessori preschool and elementary programs. This overview provides some context for understanding how the Day 1 Academies Fund eventually defines the constructs of high quality, Montessori inspired, and underserved. This review also suggests it could be useful for the Fund's stakeholders to undertake short‐term research examining the current early education options of families with low incomes living in low‐access‐to‐Montessori states as well as long‐term research aimed at expanding the research base on the effects of Montessori programs aimed at preschoolers.
... Hobbs (2008) showed that the academic achievement in reading and mathematics of Montessori schools was higher than students' achievements in non-Montessori schools. This was confirmed by Mallett (2013), whose study found that the academic achievement of Montessori students from the first and second grades is similar to the academic achievement of non-Montessori students from the fourth and fifth grades. However, this result is not supported by other previous studies. ...
... Ahmed (2004) suggested that stimulating student motivation before implementing educational activities effectively encouraged them to discover and learn and raised their academic achievement. Mallett (2013) focused his study on comparing the academic achievements between Montessori students and non-Montessori students. The results of the study indicated that the achievement of Montessori students in the first and second grades was similar to that of the fourth and fifth grades students in non-Montessori schools. ...
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This study investigated the effect of using activities based on the Montessori approach in science academic achievement of the fourth grade students. A quasi-experimental design was used wherein the students were equally divided into two groups: the experimental and the control group. Both groups consisted of 31 students. To achieve the aim of the study, Montessori Hall has been set up with six dimensions, and each corner has several shelves comprised different materials used for conducting the science activities. In addition, a teacher guide was prepared to be used by the teacher to implement the Montessori approach for the experimental group. Finally, an achievement test that consisted of seven multiple choice questions (MCQs) and five short answer questions was constructed and administered to both study groups. The results of the study indicated that there were statistically significant differences at the level of significance (P ≤ 0.05) between the mean values of the experimental and the control groups in the academic achievement in favor of the experimental group. In light of the study results, the study recommends holding training workshops for teachers on how to use the Montessori approach in teaching science classes.
... Montessori eğitiminde sınıflar, çocukların (birbirlerini gözlemleyerek) farklılıkları ayırt etmelerine ve işbirliğine (büyük çocukların küçük çocuklara rol-model olmalarıyla) fırsat sağlayacak şekilde karma yaş gruplarından oluşmaktadır (Lillard ve Else-Quest, 2006;Mallett, 2013). Burada çocuklar diğer arkadaşlarının yardımını isteyebilir; sınıfta bulunan daha büyük bir çocuk / lar küçük olan arkadaşlarına yardım etmek isteyebilirler (Korkmaz, 2005). ...
... Diğer taraftan Montessori sınıflarında her materyalden bir tane vardır. Böylece çocuklar o materyali kullanmak istediklerinde, başkalarının işinin bitmesini beklemekte ve başkalarının işlerine saygı duymayı öğrenmektedirler (Armstrong, 1999;Edwards, 2003;Mallett, 2013;Temel, 1994). ...
... Public Montessori schools have shown positive outcomes for students from diverse racial and class backgrounds (Ansari & Winsler, 2014; Brown, 2016; Dohrmann, Nishida, Gartner, Lipsky, & Grimm, 2007; Lillard & Else-Quest, 2006; Mallett & Schroeder, 2015). A quasiexperimental design compared the performance on math and reading standardized state tests across third-grade Black students at public Montessori schools, traditional schools, and other choice schools and found that the students at the Montessori school had significantly higher reading scores (Brown, 2016). ...
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As the Montessori Method continues its expansion in public education, a social justice lens is needed to analyze its contributions and limitations, given the increase in racial and socioeconomic diversity in the United States. Furthermore, much of the work in Social Justice Education (SJE) focuses on classroom techniques and curriculum, overlooking the essential work of school administrators and parents, whose work significantly influences the school community. The current study applied an SJE framework to the efforts of one urban, socioeconomically and racially integrated Montessori charter school. We examined the extent to which SJE principles were incorporated across the school community, using an inductive, qualitative, case-study approach that included meetings, surveys, focus groups, and interviews. Administrators quickly adopted a system-wide approach, but parents—often color-blind or minimizing of the relevance of race—consistently resisted. Study results imply a continued need for an institutional approach, not solely a classroom or curricular focus, when integrating social justice into Montessori schools.
... While a number of studies have featured racially and socioeconomically diverse public Montessori student samples, researchers frequently have not disaggregated data by race, making it difficult to evaluate academic and noncognitive outcomes for students of color (Dohrmann et al., 2007;Duax, 1989;Ervin, Wash, & Mecca, 2010;Lillard & Else-Quest, 2006;Lopata et al., 2005;Mallett & Schroeder, 2015;Moody & Riga, 2011). Public Montessori leaders around the country have reported strong academic gains and high graduation rates for students of color in their programs (East Dallas Community Schools, 2010; Moody & Riga, 2011), but the widespread racial achievement gaps in American public education have also been found in public Montessori schools (Mallett, 2014). ...
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Students of color comprise a majority in public Montessori school enrollments around the United States, and practitioners are often asked for evidence of the Montessori Method’s benefits for these students. This article examines the relevant literature related to the experiences of students of color in public Montessori schools. Research finds Montessori education offers both opportunities and limitations for students of color in attending diverse schools, developing executive functions, achieving academically, accessing early childhood education and culturally responsive education, minimizing racially disproportionate discipline, and limiting overidentification for special education. Public Montessori education’s efficacy with students of color may be limited by several factors: the lack of diversity of the teaching staff and culturally responsive teacher education, schools that struggle to maintain racially diverse enrollments, and the challenge of communicating Montessori’s benefits to families with alternative views of education. The review concludes with directions for future research.
... Montessori's educational background in medical department of Rome University introduced her to the scientific method and the importance of clinical observation (Mallet, 2015). In the medical department, she studied clinically to observe, diagnose patients' illness and determine their recovery. ...
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This study examined critically Montessori’s concepts on early childhood education through Islamic Psychology perspective. This research used qualitative methodology with a literature approach. The results showed that (1) Montessori’s method pays more attention to the cognitive aspect of children development while children potential doesn’t only consist of cognitive, affective, and psycho-motoric aspects, but also spiritual one; (2) Reinforcement are not needed in Montessori’s method, while in Islamic Psychology, rewards can increase children's learning and punishment is needed to make children become disciplined in carrying out the rules; (3) Learning environment should be structured, in order, realistic and natural. This concept is suitable for upper class educational institutions but it would be difficult for middle-low income groups since the materials required by Montessori’s method is expensive enough. (4) Parents and teachers are required to become observers and interpreters. This role may pose problem on the part of parents and teachers since not all parents and teachers have criteria to act as is it expected by Montessori’s method.
... In particular, Montessori participants demonstrate stronger academic skills, social-behavior, and executive functioning than children who attend more conventional educational programs. Likewise, students who experience Montessori education in the older grades also demonstrate stronger school performance (Culclasure et al., 2018;Dohrmann et al., 2007;Lillard & Else-Quest, 2006;Rathunde & Csikszentmihalyi, 2005); and these benefits extend to low-income children and children of color (Ansari & Winsler, 2014;Brown & Lewis, 2017;Culclasure et al., 2018;Dohrmann et al., 2007;Mallett & Schroeder, 2015). ...
Article
This study used covariate adjusted regression techniques to compare the third-grade outcomes of low-income Latinx children who attended Montessori pre-K programs (n = 161) with those who graduated from more conventional programs (n = 4975) in Miami-Dade County, Florida. Children who experienced one year of Montessori education demonstrated stronger pre-academic skills at the end of pre-K and, in turn, performed better on standardized assessments of math and reading in third grade than those who did not. No differences emerged in students’ identification as gifted and talented nor in third-grade GPA. Taken together, these findings suggest that the benefits of one year of Montessori at age 4 may carry forward over time and to the extent that they do, these benefits are attributed to the fact that Montessori graduates entered kindergarten more ready academically. At the same time, however, the persisting benefits of Montessori were 60–70% smaller four years after program exit and were less robust than the end of pre-K outcomes.
... Several studies also concluded that the Montessori method was effective for learning [7]; [8]; [9]. From the explained strengths, this research developed a Montessori-based Javanese script learning model. ...
... Within this framework, the materials form the fundamental structure of Montessori model (Greg, 2002). Montessori approach contributes individual learning of the children and discovery of their environments through teaching materials (Mallett & Schroeder, 2015). Thus, according to Piaget, the most suitable environment for a child's learning can be provided through rich materials and possessing of discovery freedom of these materials (Andrews, 2012). ...
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This study used a parallel mixed method approach to evaluate the instructional materials that pre-service teachers developed in their Instructional Technologies and Material Development course. The study group was composed of 10 different instructional materials developed by 2 nd year students enrolled in Faculty of Education during their Instructional Technologies and Material Development course during the 2018-2019 academic year. Additionally, 16 preschool education majors in their 2 nd year also enrolled in this course volunteered to evaluate the instructional materials. The data collection tool used in this research was the Instructional Materials Evaluation Form. The study's data were analyzed using a Many-facet Rasch Model and NVivo. The study found there to be differences both in the instructional materials developed during the course and in the criteria used to evaluate them in terms of severity and generosity. Furthermore, both the qualitative and quantitative findings revealed that pre-service teachers experienced difficulties fulfilling some, but not all criteria while developing their instructional materials
... In a study regarding the effectiveness of the teaching of the Montessori method, it was found that students whose education is based on the Montessori method, display higher performance in maths, highly developed critical thinking, problem-solving skills, as well as generally more adaptability in the classroom compared to their peers whose education entails traditional techniques (Faryadi 2017). In the same direction, remarkable differences in the mathematical performance of students of higher grades also arose from research results from Dohrmann et al. (2007), Lillard (2012) and Mallett and Schroeder (2018). On a socio-emotional level, relevant international researches have shown that the Montessori child has a positive self-image (Glenn 2003, Papanastasiou, Anagnostopoulou, and Parousi 2017, 1005. ...
Article
According to Montessori, children learn more effectively when they discover knowledge on their own, through spontaneous exploratory learning and experiential approach to knowledge, focusing primarily on trusting the child and respecting his exceptional capabilities and skills. The Montessori educational approach was implemented in a public preschool setting in North Greece. Two years after the implementation of the Montessori approach, parents were invited to participate in focus groups interviews. According to parents’ views, children gained confidence in mathematics and reading stories by their own, cooperated more easily and resolved problems with maturity. The data indicates that in such an environment, the classroom becomes productive and the children individually give their personal interpretation of the information offered to them.
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Con este trabajo de ciencia, Velarde nos acerca a cuestionamientos actuales, perennes y de la ciencia ficción. Velarde teje una historia cautivante de lo que ella ha llamado la Era artificial, y presenta las predicciones sobre el impacto tecnológico gracias a los avances de la inteligencia artificial.
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The purpose of this study was to investigate the Montessori initiative that has been adopted into the public school system in America, focusing on its quality, original purpose, successes, challenges, and the way forward. The study was based on the experiences of teachers in public Montessori schools in New York city. The schools were formerly traditional public schools that had converted to Montessori. The participating schools had a student body between 250 and 800 and a teaching and administrative staff between 12 and 40. Qualitative research methods interview data were collected by phone or face-to-face from 8 teachers working in 4 different public Montessori schools in Queens and Brooklyn, New York City. The participants were selected using a convenience sampling technique. All schools had adequate infrastructure to carter for students in a public school setting but, more classrooms were needed to reduce the population sizes in each classroom. The schools had libraries, playgrounds, ICT labs and other facilities that aided learning. Qualitative data analysis methods were used in classifying the data into themes which were analyzed, and conclusions drawn. The findings also indicated that all staff from the public schools has been Montessori trained. The public schools ran full Montessori programs and not blended Montessori/traditional public school programs as indicated by the literature. It also came to light that the teachers were satisfied with their working conditions. They had seen improvements in the program over time and were optimistic about continued improvements. They were confident that the initiative had come to stay, and their schools would be able to match the standards of the more established Montessori private schools in a few years to come.
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The low level of reading comprehension in elementary school students can certainly affect their learning motivation in the learning process. To overcome this problem, this study aims: to investigate the effect of the Montessori-based Big Book on understanding Early Reading Skills and Learning Motivation. Quasi-experimental design was applied in this study. There were 26 students (14 males and 12 females) from SDN Pucang 4 as an experimental group and 23 students (13 males and 10 females) from SDN Pucang 2 were included as a control group. Data analysis in this study used an independent sample t-test with a significance level of 0.05. The results showed that students in the experimental group had higher scores better than the control group. This shows that the Montessori-based Big Book significantly promotes understanding of Early Reading Skills and Learning Motivation in the experimental group compared to control group students.
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INTRODUCTION In this paper, we discuss the historical roots and the practical uses of constructivism in the mathematics classroom. Constructivism is the popular, yet mildly controversial belief that students construct their own knowledge through self-modification of cognitive structures. This self-modification is a largely unconscious, yet goal-directed, process by which the student reacts to a cognitive disturbance by changing how he or she thinks about a concept to accommodate the novel piece of information, thus relieving the cognitive disturbance. Essentially, this means that when the student encounters a hard problem, the student (ideally) reacts by thinking about it until it makes sense. This challenges the classic behaviorist model where a student is presented with stimuli (problems, exercises, etc.) and shown how to achieve a certain response. The behaviorist model requires some sort of external reward. In contrast, the main tenet of constructivism is that no external reward is necessary; rather, the "comfort" of the newly modified cognitive structure is rewarding in itself. Constructivism is a part of several psychological theories. The historical roots of constructivism as a psychological theory are most commonly traced to the work of Jean Piaget, although there are some elements of Piaget's constructivism that come from the early Gestalt psychologists. As collegiate mathematics education teachers and researchers, we have much experience with constructivism as both a research paradigm and a teaching method. The success of constructivism, both as a pedagogical technique and as a psychological theory, provides converging evidence of its utility. We now discuss these two facets in detail. CONSTRUCTIVISM AS PEDAGOGY The view of constructivism as a psychological theory tells us much about how students learn mathematics. Using this information, many teachers have begun to think about exactly how they conduct their mathematics classrooms. The standard model for mathematics teaching has long been the lecture, as exemplified in Krantz (1999, p. 12), where he says, "Lectures have been used to good effect for more than 3000 years." While no one will probably deny that they have seen some very effective lectures in their educational experience, the modern thought is that a good majority of lectures tend to be rather ineffective, especially in the mathematics classroom. As Dubinsky (1999) points out, how do we really know what the classroom style of Newton was like? There seems to be no historical documentation pointing to the exact teaching style of these great mathematicians. The use of constructivism in the mathematics classroom has many variations. The one thing that these variations have in common, however, is the central role of the student in the learning process. In the following, we will present some examples of classroom events that demonstrate the student-centered constructivist approach.
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Quinnipiac UniversityIn the past few decades, a constructivist discourse has emerged as a very powerfulmodel for explaining how knowledge is produced in the world, as well as howstudents learn.' For constructivists like Joe Kincheloe (2000) and Barbara Thayer-Bacon (1999), knowledge about the world does not simply exist out there, waitingto be discovered, but is rather constructed by human beings in their interaction withthe world. "The angle from which an entity is seen, the values of the researcherthat shape the questions he or she asks about it, and what the researcher considersimportant are all factors in the construction of knowledge about the phenomenonin question" (Kincheloe, 2000, 342). Thayer-Bacon (1999) invoke a quilting beemetaphor to highlight the fact that knowledge is constructed by people who aresocially and culturally embedded, rather than isolated individuals. To assert thatknowledge is constructed, rather than discovered, implies that it is neither indepen-dent of human knowing nor value free. Indeed, constructivists believe that what isdeemed knowledge is always informed by a particular perspective and shaped byvarious implicit value judgments.According to Mark Windschitl (1999), constructivism is based on the assertionthat learners actively create, interpret, and reorganize knowledge in individualways. "These fluid intellectual transformations," he maintain, "occur when stu-dents reconcile formal instructional experiences with their existing knowledge,with the cultural and social contexts in which ideas occur, and with a host ofother influences that serve to mediate understanding" (752). In this view, teach-ing should promote experiences that require students to become active, scholarlyparticipators in the learning process. Windschitl (1999) goes on to note that "suchexperiences include problem-based learning, inquiry activities, dialogues with
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