ethanporcaro/eric-fulltext-meta huggingface dataset:
Educational Equity and Quality in K-12 Schools: Meeting the Needs of All Students
Author: Thompson, Doris L.
Date: 2018-00-00
Type: Journal Articles
Subjects: Educational Quality,Equal Education,Elementary Secondary Education,Student Needs,Educational Practices,Disadvantaged Youth,Poverty,At Risk Students,Educational History,Educational Change,Educational Legislation,Federal Legislation,Teacher Qualifications,Culturally Relevant Education

This paper discusses the importance of equity and quality education in K-12 schools and how employing equity and quality strategies in classroom instructional practices and school culture can positively change children's lives. Educational achievement is a matter of the home, school, and community working in concert to build confidence in a child's life. Without this personal confidence, the child will not perform to her ability and slump down into a state of despair and hopelessness. Heckman (2008) makes a case for investing in children at risk. In a paper titled &quot;The Case for Investing in Disadvantaged Young Children&quot;, he cites 15 points that reduce inequity and raise productivity in schools. This paper examines some of these points and offers additional evidence to broaden the points of reference. A secondary purpose of this paper is to examine select research findings of the Organization for Economic Co-operation and Development (OECD) report titled Equality and Quality in Education: Supporting Disadvantaged Students and Schools.
Evaluation of Teaching Methods to Improve Reading Performance of English Language Learners
Author: Robinson, Joyce M.
Date: 2018-00-00
Type: Journal Articles
Subjects: English Language Learners,Teaching Methods,Reading Achievement,Grade 2,Elementary School Students,Reading Instruction,Phonics,Learning Theories,Constructivism (Learning),International Schools,Grade 1,Whole Language Approach,Standardized Tests,Instructional Effectiveness

This paper presents an evaluation of two reading methods, phonics-based instruction and whole language learning, for English Language Learners (ELLs) and discusses the learning theories, behaviorism and constructivism that are associated with each method, respectively. The study took place in a K-12 international school, with 110 Grade 1 subjects and 83 Grade 2 students. The author's earlier preliminary investigation of ELL reading teaching methods in the same international school, during the previous year, prompted this paper's follow-up analysis. At issue was a significant decrease in reading achievement of Grade 2 classes after changing the Grade 1 reading curriculum from a phonics-based approach to one of whole language learning. In the year following the whole language in reading classes, the phonics program returned. For purposes of this study, three Grade 1 classes were observed to observe reading achievement based on the different reading methods, including comparisons of whole language with two intensities of phonics instruction. The measurement of reading performance included standardized tests for reading achievement. Statistical analysis used t-tests and one-way ANOVA. The study found that students in Grade 1 profited significantly from having intensive phonics-based instruction as a major part of the reading program. Also, Grade 2 students with accommodating teaching methods in the early years of schooling can make important gains after significant setbacks.
Teachers&apos; Explanations of Learners&apos; Errors in Standardised Mathematics Assessments
Author: Shalem, Yael
Date: 2014-00-00
Type: Journal Articles
Subjects: Pedagogical Content Knowledge,Error Patterns,Standardized Tests,Mathematics Tests,Evaluation Criteria,Evaluative Thinking,Mathematics Teachers,Usability,Answer Keys

With the increased use of standardised mathematics assessments at the classroom level, teachers are encouraged, and sometimes required, to use data from these assessments to inform their practice. As a consequence, teacher educators and researchers are starting to focus on the development of analytical tools that will help them determine how teachers interpret learners' work, in particular learners' errors in the context of standardised and other assessments. To detect variation and associations between and within the different aspects of teacher knowledge related to mathematical error analysis, we developed an instrument with six criteria based on aspects of teachers' knowledge related to explaining and diagnosing learners' errors. In this study we provide evidence of the usability of the criteria by coding 572 explanations given by groups of mathematics educators (teachers and district officials) in a professional development context. The findings consist of observable trends and associations between the different criteria that describe the nature of teachers' explanations of learners' errors.
Mathematics-for-Teaching: Insights from the Case of Annuities
Author: Pournara, Craig
Date: 2014-00-00
Type: Journal Articles
Subjects: Pedagogical Content Knowledge,Preservice Teachers,Mathematics Teachers,Mathematics Instruction,Mathematical Concepts,Money Management,Secondary School Mathematics,Secondary School Teachers,Credit (Finance),Mathematical Formulas

Shulman's notations of subject matter knowledge (SMK) and pedagogical content knowledge (PCK) have been very influential in education research on teachers' knowledge for teaching. However, there is little empirical evidence in support of these as separate analytical constructs. Furthermore, attempts to distinguish SMK and PCK highlight the complex and multidimensional nature of teachers' knowledge and hence the difficulty of separating SMK and PCK. The author adopts the notion of mathematics-for-teaching (MfT) and argues that teachers' knowledge for teaching annuities comprises knowledge of mathematical aspects, knowledge of pedagogical aspects and contextual knowledge of finance. Drawing from a larger study in which the author taught a financial mathematics course to pre-service secondary mathematics teachers, four examples of teachers' knowledge for teaching annuities are identified, each of which illustrates how knowledge of mathematics, knowledge of pedagogy and contextual knowledge of finance are intertwined.
Number Sense of Final Year Pre-Service Primary School Teachers
Author: Courtney-Clarke, Magret
Date: 2014-00-00
Type: Journal Articles
Subjects: Numeracy,Mathematics Instruction,Teaching Methods,Elementary School Teachers,Preservice Teachers,Student Attitudes,Pedagogical Content Knowledge,Correlation,Learning Motivation,Elementary School Students,Low Achievement,Standardized Tests,Mathematics Tests,Questionnaires,Self Efficacy,Teaching Skills,Foreign Countries

Number sense studies have indicated that the development of number sense should be the focus of primary school mathematics education. The literature review revealed that learner performance is linked to teacher subject knowledge and that teachers' confidence in doing and teaching mathematics influences the way they teach and their willingness to learn mathematics. This study was motivated by the poor performance of Namibian primary school learners in both national and international standardised assessment tests and explored the number sense of 47 final-year primary school pre-service teachers (PSTs) in Namibia. The data in this mixed method research design were obtained from a number sense questionnaire, a written computations questionnaire, a mental calculations questionnaire and the McAnallen confidence in mathematics and mathematics teaching survey (MCMMTS). Six PSTs, randomly selected from the 47 participants, were interviewed to determine their use of number-sensible strategies. The overall results of this investigation revealed that the final year primary school PSTs demonstrated limited number sense and possessed very few of the indicators of number sense. Unexpectedly, the confidence survey showed that they were confident in their ability to do and to teach mathematics. This study exposed one reason for the low standards of performance of Namibian learners in mathematics and the lack of improvement over the last few decades. It indicates a need for teacher training institutions to identify the mathematics that teachers should know and the ways in which teacher understanding of subject content has to be transformed to enable them to develop the number sense of primary school learners.
Mathematical Literacy Teachers&apos; Engagement with Contextualised Income Tax Calculations
Author: Bansilal, Sarah
Date: 2014-00-00
Type: Journal Articles
Subjects: Numeracy,Mathematics Teachers,Taxes,Inservice Teacher Education,Computation,Teacher Attitudes,Interviews,Teaching Methods,Beginning Teachers,Mathematics Skills,Algebra,Foreign Countries,Mathematics Instruction

This study focuses on teachers' engagement with tasks based on the income tax tables issued by the South African tax authorities. The participants in the study are a group of 37 teachers who were enrolled in an in-service programme for Mathematical Literacy teachers. The purpose of the study is to explore the teachers' interpretation and use of the rule used to calculate income tax. Data were generated from written responses of the teachers to three tasks, as well as follow-up interviews with eight of the participants. The findings indicate that some teachers (8%) did not recognise any of the demands inherent in the income tax rule that they teach to their learners. Most teachers (54%) were in the novice category, showing that they met some of the demands but need some help in carrying out the rule fluently. A further 32% were able to use the rule to work out the tax given various input incomes, but could not use the rule to find the input income when given the tax output, because they did not have the necessary algebraic skill.
Exploring the Use of a Dynamic Online Software Programme in the Teaching and Learning of Trigonometric Graphs
Author: Naidoo, Jayaluxmi
Date: 2014-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Trigonometry,Secondary School Students,Teaching Methods,Case Studies,Computer Software,Grade 10,Foreign Countries,Worksheets,Student Attitudes,Graphs,Scores,Mathematics Tests,Learning Motivation,Computer Assisted Instruction,Instructional Effectiveness

Trigonometry is an important section in mathematics that links algebraic, geometric and graphical reasoning. Many secondary school learners are not familiar with these types of reasoning; thus, trigonometry presents a challenge for these learners. The traditional 'chalk and talk' method of teaching trigonometry is used by many teachers; however, this article is based on a case study that explores the innovative use of a dynamic online software program in the teaching and learning of Grade 10 trigonometric graphs. The participants in this study were 25 Grade 10 mathematics learners from one school in the south of Durban, KwaZulu-Natal, South Africa. Data were collected by using two trigonometry worksheets, semi-structured interviews with selected learners and lesson observations. The worksheets were constructed based on the following focus areas: behaviour of graphs, interpretation of graphs, modelling and overall performance of the learner. In all focus areas, the participants' scores improved significantly when working within the dynamic online environment. Further analysis revealed the following five themes: easy access, learners in control, technology is the future, motivation and meaningful interaction. These findings would be of interest to mathematics teachers, learners, curriculum developers and mathematics teacher educators.
Mathematics, Curriculum and Assessment: The Role of Taxonomies in the Quest for Coherence
Author: Long, Caroline
Date: 2014-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Problem Solving,Foreign Countries,Mathematics Achievement,International Assessment,Mathematics Tests,Achievement Tests,Mathematical Concepts,Mathematics Teachers,Secondary School Mathematics,Curriculum Design,Educational Objectives,Classification,Grade 9

A challenge encountered when monitoring mathematics teaching and learning at high school is that taxonomies such as Bloom's, and variations of this work, are not entirely adequate for providing meaningful feedback to teachers beyond very general cognitive categories that are difficult to interpret. Challenges of this nature are also encountered in the setting of examinations, where the requirement is to cover a range of skills and cognitive domains. The contestation as to the cognitive level is inevitable as it is necessary to analyse the relationship between the problem and the learners' background experience. The challenge in the project described in this article was to find descriptive terms that would be meaningful to teachers. The first attempt at providing explicit feedback was to apply the assessment frameworks that include a content component and a cognitive component, namely knowledge, routine procedures, complex procedures and problem solving, currently used in the South African curriculum documents. The second attempt investigated various taxonomies, including those used in international assessments and in mathematics education research, for constructs that teachers of mathematics might find meaningful. The final outcome of this investigation was to apply the dimensions required to understand a mathematical concept proposed by Usiskin (2012): the &quot;skills-algorithm,&quot; &quot;property-proof,&quot; &quot;use-application&quot; and &quot;representation-metaphor&quot; dimension. A feature of these dimensions is that they are not hierarchical; rather, within each of the dimensions, the mathematical task may demand recall but may also demand the highest level of creativity. For our purpose, we developed a two-way matrix using Usiskin's dimensions on one axis and a variation of Bloom's revised taxonomy on the second axis. Our findings are that this two-way matrix provides an alternative to current taxonomies, is more directly applicable to mathematics and provides the necessary coherence required when reporting test results to classroom teachers. In conclusion we discuss the limitations associated with taxonomies for mathematics.
Teacher Knowledge of Error Analysis in Differential Calculus
Author: Moru, Eunice K.
Date: 2014-00-00
Type: Journal Articles
Subjects: Calculus,Mathematics Instruction,Pedagogical Content Knowledge,Knowledge Base for Teaching,Mathematical Concepts,Concept Formation,Error Patterns,Specialists,Identification,Accuracy,Efficiency,College Faculty,Teacher Attitudes,Foreign Countries,Mathematics Teachers,Validity,Reliability,College Students

The study investigated teacher knowledge of error analysis in differential calculus. Two teachers were the sample of the study: one a subject specialist and the other a mathematics education specialist. Questionnaires and interviews were used for data collection. The findings of the study reflect that the teachers' knowledge of error analysis was characterised by the following assertions, which are backed up with some evidence: (1) teachers identified the errors correctly, (2) the generalised error identification resulted in opaque analysis, (3) some of the identified errors were not interpreted from multiple perspectives, (4) teachers' evaluation of errors was either local or global and (5) in remedying errors accuracy and efficiency were emphasised more than conceptual understanding. The implications of the findings of the study for teaching include engaging in error analysis continuously as this is one way of improving knowledge for teaching.
Investigating Learners&apos; Meta-Representational Competencies When Constructing Bar Graphs
Author: Mhlolo, Michael
Date: 2015-00-00
Type: Journal Articles
Subjects: Graphs,Tables (Data),Mathematics Instruction,Mathematics Teachers,Grade 11,Secondary School Teachers,Secondary School Mathematics,Statistics

Current views in the teaching and learning of data handling suggest that learners should create graphs of data they collect themselves and not just use textbook data. It is presumed real-world data creates an ideal environment for learners to tap from their pool of stored knowledge and demonstrate their meta-representational competences. Although prior knowledge is acknowledged as a critical resource out of which expertise is constructed, empirical evidence shows that new levels of mathematical thinking do not always build logically and consistently on previous experience. This suggests that researchers should analyse this resource in more detail in order to understand where prior knowledge could be supportive and where it could be problematic in the process of learning. This article analyses Grade 11 learners' meta-representational competences when constructing bar graphs. The basic premise was that by examining the process of graph construction and how learners respond to a variety of stages thereof, it was possible to create a description of a graphical frame or a knowledge representation structure that was stored in the learner's memory. Errors could then be described and explained in terms of the inadequacies of the frame, that is: 'Is the learner making good use of the stored prior knowledge?' A total of 43 learners were observed over a week in a classroom environment whilst they attempted to draw graphs for data they had collected for a mathematics project. Four units of analysis are used to focus on how learners created a frequency table, axes, bars and the overall representativeness of the graph &quot;vis-à-vis&quot; the data. Results show that learners had an inadequate graphical frame as they drew a graph that had elements of a value bar graph, distribution bar graph and a histogram all representing the same data set. This inability to distinguish between these graphs and the types of data they represent implies that learners were likely to face difficulties with measures of centre and variability which are interpreted differently across these three graphs but are foundational in all statistical thinking.
An Investigation of Mathematical Literacy Assessment Supported by an Application of Rasch Measurement
Author: Long, Caroline
Date: 2014-00-00
Type: Journal Articles
Subjects: Numeracy,Item Response Theory,Mathematics Instruction,Test Items,Test Validity,Grade 12,Secondary School Students,Secondary School Mathematics,Foreign Countries,Probability,Difficulty Level,Scores

Mathematical Literacy (ML) is a relatively new school subject that learners study in the final 3 years of high school and is examined as a matric subject. An investigation of a 2009 provincial examination written by matric pupils was conducted on both the curriculum elements of the test and learner performance. In this study we supplement the prior qualitative investigation with an application of Rasch measurement theory to review and revise the scoring procedures so as to better reflect scoring intentions. In an application of the Rasch model, checks are made on the test as a whole, the items and the learner responses, to ensure coherence of the instrument for the particular reference group, in this case Mathematical Literacy learners in one high school. In this article, we focus on the scoring of polytomous items, that is, items that are scored 0, 1, 2 … &quot;m.&quot; We found in some instances indiscriminate mark allocations, which contravened assessment and measurement principles. Through the investigation of each item, the associated scoring logic and the output of the Rasch analysis, rescoring was explored. We report here on the analysis of the test prior to rescoring, the analysis and rescoring of individual items and the post rescore analysis. The purpose of the article is to address the question: How may detailed attention to the scoring of the items in a Mathematical Literacy test, through theoretical investigation and the application of the Rasch model, contribute to a more informative and coherent outcome?
The Relational Nature of Rational Numbers
Author: Brown, Bruce
Date: 2015-00-00
Type: Journal Articles
Subjects: Correlation,Numbers,Number Concepts,Mathematics Instruction,Foreign Countries,Preschool Children,Elementary School Students

It is commonly accepted that the knowledge and learning of rational numbers is more complex than that of the whole number field. This complexity includes the broader range of application of rational numbers, the increased level of technical complexity in the mathematical structure and symbol systems of this field and the more complex nature of many conceptual properties of the rational number field. Research on rational number learning is divided as to whether children's difficulties in learning rational numbers arise only from the increased complexity or also include elements of conceptual change. This article argues for a fundamental conceptual difference between whole and rational numbers. It develops the position that rational numbers are fundamentally relational in nature and that the move from absolute counts to relative comparisons leads to a further level of abstraction in our understanding of number and quantity. The argument is based on a number of qualitative, in-depth research projects with children and adults. These research projects indicated the importance of such a relational understanding in both the learning and teaching of rational numbers, as well as in adult representations of rational numbers on the number line. Acknowledgement of such a conceptual change could have important consequences for the teaching and learning of rational numbers.
Validation of a Measure of Sustainability of School-Wide Behavior Interventions and Supports
Author: Kittelman, Angus
Date: 2019-04-00
Type: Journal Articles
Subjects: Positive Behavior Supports,Intervention,Decision Making,Capacity Building,Sustainability,School Districts,Measures (Individuals),Test Validity,Test Reliability

The purpose of this study was to evaluate the stability and validity of a measure assessing sustainability of school-wide behavior interventions, the &quot;School-Wide Universal Behavior Support Sustainability Index: School Teams&quot; (SUBSIST). We assessed the stability of the SUBSIST across 3 years of measurement. We also assessed the convergent validity of two key SUBSIST factors, Team Use of Data and District Capacity Building, with more direct measures of these constructs. Results showed stability of the measure across multiple years and statistically significant correlations when compared with other external measures. Implications for research and practice are discussed.
Problematising Current Forms of Legitimised Participation in the Examination Papers for Mathematical Literacy
Author: North, Marc
Date: 2015-00-00
Type: Journal Articles
Subjects: Mathematics Instruction,Numeracy,Apprenticeships,Foreign Countries,Grade 12,Secondary School Mathematics,Problem Solving

In this article we argue that in South Africa the current format of legitimised participation and practice in the examination papers for Mathematical Literacy restricts successful apprenticeship in the discipline of scientific mathematics and limits empowered preparation for real-world functioning. The currency of the subject, then, is brought into question. We further argue that the positioning of the subject as a compulsory alternative to Mathematics and the differential distribution of these two subjects to differing groups of learners facilitates the (re)production and sustainment of educational disadvantage. We draw on Dowling's theoretical constructs of differing domains of mathematical practice and positions and focus analysis on a collection of nationally set exemplar Grade 12 examination papers to identify legitimised forms of participation in the subject. We conclude by arguing for a reconceptualised structure of knowledge and participation in Mathematical Literacy and make preliminary recommendations in this regard.