8th Grade Mathematics Research Articles

An Analysis of Mathematics Achievements Based on Student Engagement and Attitude in Asean Countries Compared with TIMSS 2011 and TIMSS 2015

The Trends in International Mathematics and Science Study (TIMSS) is the largest and most ambitious study undertaken by the International Association for the Evaluation of Educational Achievement. About forty-two countries involved in TIMSS 2011 and thirty-nine countries involved in 2015. The 8th grade Mathematics Question are based on four content areas: (1) number; (2) algebra; (3) geometry; (4) data and chance. Investigating this particular issue through the TIMSS data files seems to provide a comprehensive source to analyse mathematics achievement of students from various angles. The aim of this paper is to analyse the mathematics achievement of 8th grade Mathematics Questions for ASEAN countries compared to TIMSS 2011 and 2015 by classifying them based on Student Engagement and Attitude. As the outcome measure, this paper used the set of four index values of student engagement and attitudes towards learning mathematics and average achievement in mathematics for TIMSS 2011 and TIMSS 2015. The ASEAN countries that involves both in TIMSS 2011 and TIMSS 2015 are Malaysia, Singapore and Thailand. Besides, the study also seek for significant value between each content areas with student perception and valuing of mathematics. All differences described in this study are statistically significant at the 0.05 level. Results from the TIMSS have recently captured the attention of the government and once again focused the nation on matters of mathematics teaching and learning. In general, the TIMSS results indicate a pervasive and intolerable mediocrity in mathematics teaching and learning in the middle grades and beyond.

Want to Improve Math Scores? An Empirical Assessment of Recent Policy Interventions in Canada

The Canadian provinces have implemented various strategies aimed at improving kindergarten through 12th-grade mathematics performance. There is no clear evidence which, if any, of these strategies improve achievement scores. We apply hierarchical linear modelling to the 2012 Program for International Student Assessment data to isolate the effects of policy interventions. We find that efforts to improve learning conditions can be worthwhile, but their effects are not as substantial as a school’s socio-economic status composition, which elevates or depresses the academic achievements of all students. As barriers to school choice come down, ambitious parents will resort to active school choice, a strategy that may reduce social equity.

An Examination of the Activities in 8th Grade Mathematics Textbooks Based on the Levels of Cognitive Demand

In this study, the cognitive demand levels of the activities in 8th grade mathematics textbooks were attempted to be identified and the distribution of these textbooks was compared based on the cognitive demand levels of the activities. The method used in the research was document analysis. In order to collect the data, a total of 90 activities in two 8th grade mathematics textbooks approved by the Education Board of the Ministry of National Education were examined. A descriptive analysis method was used to analyze the data. Findings of the study demonstrated that the number of activities in both textbooks approximated to each other. Although the reviewed textbooks were approved by the Board of Education as textbooks, it was observed that the cognitive demands of the activities provided concentrated on levels that are connected and are unconnected to procedures and that the textbooks demonstrated a differentiation based on cognitive demand levels when compared to each other. In this respect, students educated with different textbooks may have different learning outcomes.

DESIGN AND DEVELOPMENT OF AN EDUCATIONAL DIGITAL GAME BASED ON MATHEMATICS COURSE TRANSFORMATION GEOMETRY

The digital gaming industry is growing rapidly both economically and in terms of the masses it is influencing. This growth in the sector makes digital games effective in culture and education. In order to use this effect in a beneficial way, it is necessary to be included in the sector. In this research, 8th grade mathematics curriculum a game called “Simetri” has been developed for the purpose of reinforcing the acquisitions of the transformation Geometry subject. The works and processes performed during the development are discussed in this article. The basic structure of the game; it is based on the process of automatically generating the image after the correct clicking of the corners of the image which will result from the reflection of the polygons drawn on the squared paper, dot paper and the coordinate plane with respect to the determined axis of symmetry. There are different difficulty stages within the game and separate levels within these stages. There is also a scoring system in the game and new records are kept. Although the game is mainly based on the concept of reflection, it is open to further development of the concept of translation and the solution of more complex problems.

Comparing the education systems of Central-Eastern European countries – policies and curricula

My study compares education systems in the East-Central European region from the aspect of regulation and curriculum. Curriculum regulation is one of the main tools of education management. Each country has its own legislation in public education, having centrally developed curricula or standards. In my research, I am looking for the common features of these countries (Hungary, Romania, Serbia, Croatia, Slovenia, Austria, Slovakia, Czech Republic, Poland), which unify the region and assume similar functioning. My main question is: can we talk about unity in the regulation of education and curricula? I compared these countries via the following aspects: Types of regulation and curriculum; Content of mathematics curricula; Evaluation system and exams. My research is based on document analysis. I rely on primary sources (educational laws, national curricula, regulations) and secondary sources (country reports, OECD publications). In my comparison, I identified the consistent aspects of the region, such as the strong central regulation through legislation, although the implementation of the laws is at a lower level leading to a different centralization in enforcement and control. Moreover, each country has a national core curriculum and local/school curricula providing the freedom of institutions, but its scale is different. In the second part of my study, I compare the mathematics curricula of the countries, since that subject is part of the international assessments (PISA, TIMSS). I point out the differences that may cause different results in international studies; the number of math lessons in primary school (Austria has 150 hours of mathematics a year, Hungary has only 81, and other countries have around 105 hours), and the different contents of 8th grade mathematics education (for example, in Romania, the topic of probability calculation does not appear in this grade). The results of my research help to illustrate the functioning and differences of the educational systems of the region and point out what makes them still unified, even though they have progressed in different ways.

The Strategy the Use of False Assumption and Word Problem Solving

The paper describes one problem solving strategy – the Use of false assumption. The objective of the paper is to show, in accordance with Phylogenesis and Ontogenesis Theory, that it is worthwhile to reiterate the process of development of the concept of a variable and thus provide to pupils one of the ways helping them to eliminate usual difficulties when solving word problems using linear equations, namely construction of the equations. The paper presents the outcomes of a study conducted on three lower secondary schools in the Czech Republic with 147 14–15-year-old pupils. Pupils from the experimental group were, unlike pupils from the control group, taught the strategy the Use of false assumption before being taught the topic Solving word problems. The tool for the study was a test of four problems that was sat by all the involved pupils three weeks after finishing the topic “Solving word problems” and whose results were evaluated statistically. The experiment confirmed the research hypothesis that the introduction of the strategy the Use of false assumption into 8th grade mathematics lessons (14–15-year-old pupils) helps pupils construct equations more successfully when solving word problems.

Children’s reasoning about decimals and its relation to fraction learning and mathematics achievement.

Reasoning about numerical magnitudes is a key aspect of mathematics learning. Most research examining the relation of magnitude understanding to general mathematics achievement has focused on whole number and fraction magnitudes. The present longitudinal study (N = 435) used a 3-step latent class analysis to examine reasoning about magnitudes on a decimal comparison task in 4th grade, before systematic decimals instruction. Three classes of response patterns were identified, indicating empirically distinct levels of decimal magnitude understanding. Class 1 students consistently gave correct responses, suggesting that they understood decimal properties even before systematic decimal instruction. Class 2 students were accurate when a 0 immediately followed the decimal, but were inaccurate when a zero was added to the end of the decimal string, suggesting a partial understanding of place value; their performance was also negatively influenced by a whole number bias. Class 3 students showed misunderstanding of both place value and a whole number bias. Class membership accurately predicted 6th grade mathematics achievement, after controlling for whole number and fraction magnitude understanding as well as demographic and cognitive factors. Taken together, the findings suggest students may benefit from instruction that emphasizes decimal properties earlier in school. (PsycINFO Database Record (c) 2019 APA, all rights reserved)

Exploring Resilience in Latina/o Academic Outcomes: A Latent Class Approach

The purpose of this study is to explore the relationship between various protective factors with academic outcomes of Latina/o high school students. We use two groups of protective influences, individual and family, and their relationship to 12th grade mathematics achievement, dropout rates, and enrollment in post-secondary education. Latent class analysis was used to identify academic protective profiles, or latent groups/classes, among high school Latina/o students (N = 1610) and assess group differences with respect to gender, SES, immigrant status, student’s native language, preschool attendance, and 10th grade mathematics. Results indicated the presence of four academic protective groups, which differed with respect to academic discussions with parents, and attitudes about mathematics. The four classes are compared with respect to academic outcomes and differences are discussed as well as implications for practice.

The Language Used in the 8th Grade Mathematics Textbook

This study aimed at identifying the form of the language, which is expressive of the mathematics and mathematics learner in the 8th grade mathematics textbook. The results showed that the mathematics textbook tends to exhibit an absolute, symbolic, mathematics specific image and a negative image of the mathematics learner as just who executes the orders (scribbler), rather than a thinker or engaged in authentic problem solving. Possibly, these two images may explain the difficulties and problems the students encounter while learning mathematics.

Co-teaching Effectiveness: Students’ Achievement in Mathematical Proficiencies and Content Strands

In Pakistan Mathematics is being taught by single teacher. In contrast co-teaching has shown its positive effects on students’ academic achievement in Mathematics. Keeping in view the importance of co-teaching, this study was aimed at examining the co-teaching effectiveness to enhance students’ scores in mathematics. An experimental research design, Solomon Four Group was applied in this study to conduct an experiment. A school in the public sector was selected on convenient basis with due permission of headmaster. There were 118 students studying in that school at 8th grade situated in Sargodha district. A teaching module of mathematics was developed on two content strands of 8th grade mathematics i.e. algebra & geometry. The duration for one lesson was one hour. There were 20 lessons in the module and were validated by two mathematics experts. Students’ achievement was measured by using an achievement test of mathematics. Pakistan National Educational Assessment System had developed and validated the items. Data were analyzed by applying Mean, Standard deviation, and independent sample t-test. Co-teaching was found to be more effective than single teacher’s teaching in enhancing students’ achievement score in algebra and geometry with mathematical proficiencies. It was recommended that a topic on co-teaching should be included in courses preparing teachers of Mathematics.

Multiple Representations in 8th Grade Mathematics Textbook and the Extent to which Teachers Implement Them

This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and transitions among them in 8th Grade Mathematics Textbook. An observation method was used to analyses the teacher practices (n=35 observations), and record the representations and transitions. The results showed that there was an existence of symbol and verbal representations in the textbook and teachers' implementation. Meanwhile, the other three representations (pictures and figures, models and Cutters, and life situations) and the transactions between them were at low rates in the textbook and teachers' implementation.

Mathematics teachers’ specialized knowledge: a secondary teacher's knowledge of rational numbers

ABSTRACTRecognising teachers’ knowledge as one of the main factors influencing their practices and student learning, we aim to contribute to obtaining a better and deeper understanding of the specificities of teachers’ mathematical knowledge. A case study involving one 8th-grade Chilean mathematics teacher is presented in the context of rational numbers. Using video and audio recordings of classroom practices, questionnaires, and an interview, we sought to characterise, and better understand the content of the Knowledge of Topics from the perspective of the Mathematics Teachers’ Specialized Knowledge (MTSK) theoretical framework. The results reveal some critical aspects that teacher education should focus on, while also identifying lost opportunities and examples of “good” practices, thus contributing to the refinement of the MTSK conceptualisation. The conclusions can be considered in a broader perspective, with implications for teacher education in other contexts.

EFFECT OF CREATIVE DRAMA METHOD ON GEOMETRY TEACHING

Geometry holds an important place in the developmental process of mathematical thinking. When geometry is the subject in mathematics lessons, it is seen by students as an unlikeable and hard to understand. It is not easy to get students who come to school with this prejudice to like the lesson and explain it. Our aim in this research is to eliminate this prejudice using right teaching methods and make mathematics a lesson attended voluntarily and with pleasure by the students. With this aim in mind, the effect of creative drama method on students’ success for the 6th grade mathematics lesson, area of triangles subject has been researched. This study has been applied on 100 students enrolled in two different state secondary schools in Aegean Region in 2017-2018 teaching term. In this study, classes are divided into two groups as control group and experimental group and a success test designed by researchers on area of triangles subject is applied to students as pretest and final test. This test consists of 7 multiple choice and 3 open ended questions. Data obtained from the test is analyzed by statistical method. After the analysis, a meaningful difference in favor of experimental group has arisen. Based on the reviews made with the students, it is noticed that the interest of students to mathematics lesson has increased as a result of creative drama applications. Article visualizations:

İlköğretim Matematik Öğretmenlerinin Hazırladıkları Testlerin Öğretim Programı Kazanımları Açısından Bir Analizi

Bu çalışma, matematik öğretmenlerinin sınavlarında sordukları soruları, İlköğretim Matematik Dersi 8. Sınıf Öğretim Programında yer alan kazanımlar ve çalışma takvimine uygunluğu açısından incelemeyi amaçlamaktadır. Bu amaçla Manisa ili Demirci ilçesinde görev yapan 13 farklı ortaokuldaki 8. sınıf matematik dersine giren 18 matematik öğretmeninin hazırlamış olduğu, 548 sorudan oluşan 30 adet sınav kâğıdı doküman analizi yöntemi ile incelenmiştir. Araştırma bulguları, soruların %88’inin 8. sınıf matematik dersi öğretim programındaki kazanımlara yönelik hazırlandığını göstermektedir. Bunun yanında, test maddelerinin bir kısmının aynı anda birden çok kazanımı ölçmeye yönelik, bir kısmının alt sınıf kazanımlarına yönelik olarak hazırlandığı, bir kısmının da çalışma takvimine göre doğru zamanda sorulmadığı belirlenmiştir. Diğer taraftan, soruların ölçtüğü kazanımların yüzdeliklerinin öğretmenlere göre önemli ölçüde farklılaştığı tespit edilmiştir.

Teacher knowledge experiment: Testing mechanisms underlying the formation of preservice elementary school teachers’ pedagogical content knowledge concerning fractions and fractional arithmetic.

Pedagogical content knowledge forms the core of teachers’ professional knowledge; it refers to knowledge about making subject matter accessible to students. Thus, the formation of pedagogical content knowledge constitutes a crucial issue for educational research and practice. We investigated the contributions of content knowledge and pedagogical knowledge to the formation of pedagogical content knowledge about fractions and fractional arithmetic in 6th grade mathematics in a between-participants study with 100 German preservice teachers. The three experimental and two control groups received 7 hr of intervention spread out over two days. We assessed participants’ pedagogical content knowledge before intervention, between the two days, after intervention, as well as at 6-week follow-up. The control groups exclusively received instruction on either pedagogical knowledge or pedagogical content knowledge; each of the experimental groups embodied a specific hypothesis about the formation of pedagogical content knowledge. Providing support for a mechanism of amalgamation, a combination of instruction on content knowledge and pedagogical knowledge produced small but statistically significant growth in pedagogical content knowledge. Similarly, instruction on content knowledge exclusively was sufficient to cause small but statistically significant growth in pedagogical content knowledge. Prior instruction on content knowledge did not facilitate learning from instruction on pedagogical content knowledge. Nevertheless, direct instruction on pedagogical content knowledge caused medium and statistically significant growth in pedagogical content knowledge. (PsycINFO Database Record (c) 2018 APA, all rights reserved)

One curriculum and two textbooks: opportunity to learn in terms of mathematical problem solving

This paper explores how problem solving is approached in two 6th grade mathematics textbooks and national elementary mathematics curriculum in Turkey. The curriculum and textbooks’ problem solving approaches are analysed and compared in the light of three approaches of ‘teaching for, about and through problem solving’. Four learning objectives from different content areas (e.g. algebra, data processing) from the curriculum are determined and their treatments in the textbooks are specifically analysed. The analysis showed that the curriculum did not have a prescriptive stance on any one of problem solving approaches. Similarly, the textbooks also did not follow any approach faithfully. ‘Teaching for problem solving’ approach was not employed while ‘teaching through problem solving’ approach was used for only one learning objective in the textbooks. ‘Teaching about problem solving’ approach was encountered in terms of only one problem solving heuristic (table drawing). We discuss the implications of these findings and note some further research areas.

English

This study investigated the applicability of alternative assessment methods used in 4th grade mathematics curriculum in Turkey and the United States with the intent of implementing these methods more effectively in elementary schools. The sampling included six elementary schools with twelve teachers in AdA±yaman in Turkey; four elementary schools with twelve teachers in Pittsburgh, PA in the U.S. Qualitative data were gathered through document examination semi-structured observation, and semi-structured interviews; they were analyzed qualitatively. Findings indicated a similarity in the foundational resources used in both mathematics curriculua. The observations revealed that although both groups of teachers professed using the assessment methods, teachers in the U.S. applied the methods in their classrooms, while teachers in Turkey did not. The interviews disclosed factors preventing the application of alternative methods, particularly among Turkish teachers, including time, the availability of other methods, and the enormous pressure to “teach to the test.” Key words: Alternative assessment, mathematics, curriculum, elementary school.

Using Classroom Observation Scores Instead of Test Scores as Criterion in the Estimation of Discrimination Index

Item discrimination index, which indicates the ability of the item to distinguish whether or not the individuals have acquired the qualities that are evaluated, is basically a validity measure and it is estimated by examining the fit between item score and the test score. Based on the definition of item discrimination index, classroom observation scores were used in this study instead of test scores as the indication of having the tested quality.In the framework of the study, a 25-item multiple-choice test prepared in the context of 8th grade Mathematics Unit "Multipliers and Multiples" was administered to a total of 109 8th graders (44 females, 65 males) studying in 4 separate classrooms of Ömer Nasuhi Bilmen Secondary School in Şanlıurfa Province. Furthermore, these students’ Mathematics teachers were asked to observe and score students during the unit and the obtained observation scores were used as external criterion in estimating the discrimination index. By using this criterion, fit values estimated with the help of upper and lower groups consisting of 27% from the extremes of the criterion score distribution and biserial correlation were compared with the traditional conditions where test scores were utilized. It was found that item discrimination indices based on classroom observations were higher than those based on test scores in both of the discrimination indices estimated via upper-lower 27% groups and biserial correlation. This finding was discussed to be related to the fact that while classroom observation scores were an external validity criterion, test scores were composed of items whose discrimination values were calculated. The finding also demonstrated that classroom observation scores were more rigid and eliminative than test scores in terms of discrimination.

Four mediation models of teacher expectancy effects on students\u2019 outcomes in mathematics and literacy

The study tested 4 direct and 28 indirect teacher expectancy effects on students’ results in the mathematics and literacy sections of the matriculation test, and their final marks in the 12th-grade mathematics and literacy class. The following were considered as mediators: student self-esteem, their self-expectancy, and time spent learning mathematics and literacy. The study involved 1374 first year college students. Conducted path analyses revealed: (1) the total teacher expectancy effects was the strongest for final marks in mathematics, followed by test results in mathematics, test results in literacy, and final marks in literacy; (2) the direct effect was stronger than the total indirect teacher expectancy effects in the case of mathematics, while for literacy outcomes, the order of the effects was reversed; (3) the direct teacher expectancy effects were positive; the indirect effects reversed after including student self-esteem/student self-expectancy into relations between teachers’ expectancy and mathematics and literacy outcomes; (4) teachers’ expectancy was mediated most strongly by student self-esteem, time spent learning, and student self-expectancy, or by student self-expectancy and time spent learning, respectively for mathematics and literacy outcomes; (5) the impact of teachers’ expectancy was stronger than student self-expectancy for mathematics, but was the same or weaker for literacy outcomes, respectively. The obtained results were discussed in the light of the theory and results of studies concerning teacher expectancy effects.

Opportunities to learn: Mathematics textbooks and students’ achievements

This study explores how textbooks function in education. It asked whether opportunities provided in math textbooks to engage in tasks demanding different levels of understanding correlate with students’ achievements on tasks demanding equivalent levels of understanding on a standardized exam. The textbooks evaluated were two 8th grade mathematics textbooks used by students in the Arab community in Israel, showing that Textbook A makes more cognitive demands than Textbook B. The study correlated textbooks’ cognitive demand with the scores of all 8th grade students in the Arab community who completed the national math test in 2015 and studied in schools using either Textbook A or B (N=4040), while attending to mediating variables. The findings show that if a textbook provides the opportunity to engage in tasks demanding higher levels of understanding, students using this book will have higher scores. The study shows that gender and SES play an important role in how opportunities provided in textbooks interact with students’ scores. Many factors influence variations in mathematics achievements within and between nations. The findings illuminate textbooks’ ability to provide opportunities to learn mathematics. As a result, they raise new questions about how teachers use textbooks and about the role of textbooks in promoting access and equity in mathematics education. Although the work explored specific textbooks, its findings shed light on how learning opportunities relate to achievements more generally.