Student Understanding of Linear Scale in Mathematics: Exploring What Year 7 and 8 Students Know

<p>This thesis set out to undertake a curriculum review. Scale was chosen as the focus of the review because the Mathematics and Science Taskforce (1997) indicated that measurement was an area of the curriculum that needed priority attention, however comparatively little had been done to provide this by 2005. Scales are a common mathematical object. A search of many (Western) homes is likely to find a variety of scales being used for different purposes. They can be found on car dashboards, kitchen stoves, tape measures, and clocks. They will be found in graphs, newspapers, and magazines. Scales also underpin important mathematical learning over and above their everyday application to measurement and graphing. For example, concepts like gradient, rate of change, functions, and limits all rely on an understanding of scale. But how much do we know about how students learn to use scales? What does learning about scale involve? The thesis approaches the review through an exploration of student understanding of scale in the context of mathematics. It focuses on answering the question "what understanding of scales do students in Year 7 and 8 at the case study schools have?" A definition of scale is developed and is based on the mathematics to which the curriculum document indicates Year 7 and 8 students should have been exposed. This could be identified as the notion of a linear scale. Students in Years 7 and 8 were chosen because by that age the mathematics curriculum document implies students should have a good understanding of scale; at the same time, their errors and misconceptions are likely to indicate learning barriers that need to be addressed. The literature and the New Zealand mathematics curriculum were used to define a construct of scale appropriate to explore with Year 7 and 8 students. Two tests were then developed to measure understanding of that construct. Where possible, items were initially developed or adapted from the literature then, when early findings suggested new avenues for exploration, new items were developed to investigate further issues of understanding. Both tests were used at different schools in the format of a cognitive interview; Test 1 was also used at another school as a written test. Additional items were developed to use with groups of teachers in an attempt to challenge early findings; these teacher trials used a third assessment format requiring both a written answer and a written explanation of method. In Test 1 students were assessed with pairs of items. In each pair one item used a decontextualised number line, the other a measurement or graphing context promoted by the curriculum. During the cognitive interviews, the verbal responses of students were recorded on audiotape, while field notes were used to capture non-verbal data. Follow-up probe questions were used to clarify solution strategies and the understanding underlying these strategies. The written test was then used to identify if the interpretations made could be transferred. Test 2 repeated the data collection methodology from Test 1 but used a different structure within the test. In total, 45 cognitive interviews and 81 written tests were undertaken with students, while 32 teachers participated in the teacher trials. Facilities, point bi-serial correlation coefficients, and levels of significance were used to ascertain the fitness for purpose of the developed test items. Data collected during the cognitive interviews were also analysed using both qualitative and quantitative methods to ascertain patterns of response. The mathematics curriculum in New Zealand had assumed that students would develop understanding about scale from exposure to scales in measurement and graphing situations. This approach might have been appropriate if a scale was a simple (or single) object to be mastered but it is not. A scale is a mathematical tool of vast flexibility that can be applied in numerous forms to a wide range of situations. The results suggest that teaching of scale needs to be more deliberate, and also needs to be considered when curricula are designed. A high proportion of the students in the study had not developed the expected understanding of scale by Years 7 and 8. A complex series of factors were identified that impacted on how the students worked with scale. These included: their understanding of number and number symbols; their understanding of the measurement conventions that are foundational to scale; the strategies they had developed to partition unmarked intervals; their strategies to decide on the value of a partition in marked intervals; their understanding of the role of the marks and spaces on the scale; and their ability to iterate a unit. These different bodies of understanding needed to be integrated and used in a coordinated manner for the students to become effective users of scale.</p>

Student Understanding of Linear Scale in Mathematics: Exploring What Year 7 and 8 Students Know

<p>This thesis set out to undertake a curriculum review. Scale was chosen as the focus of the review because the Mathematics and Science Taskforce (1997) indicated that measurement was an area of the curriculum that needed priority attention, however comparatively little had been done to provide this by 2005. Scales are a common mathematical object. A search of many (Western) homes is likely to find a variety of scales being used for different purposes. They can be found on car dashboards, kitchen stoves, tape measures, and clocks. They will be found in graphs, newspapers, and magazines. Scales also underpin important mathematical learning over and above their everyday application to measurement and graphing. For example, concepts like gradient, rate of change, functions, and limits all rely on an understanding of scale. But how much do we know about how students learn to use scales? What does learning about scale involve? The thesis approaches the review through an exploration of student understanding of scale in the context of mathematics. It focuses on answering the question "what understanding of scales do students in Year 7 and 8 at the case study schools have?" A definition of scale is developed and is based on the mathematics to which the curriculum document indicates Year 7 and 8 students should have been exposed. This could be identified as the notion of a linear scale. Students in Years 7 and 8 were chosen because by that age the mathematics curriculum document implies students should have a good understanding of scale; at the same time, their errors and misconceptions are likely to indicate learning barriers that need to be addressed. The literature and the New Zealand mathematics curriculum were used to define a construct of scale appropriate to explore with Year 7 and 8 students. Two tests were then developed to measure understanding of that construct. Where possible, items were initially developed or adapted from the literature then, when early findings suggested new avenues for exploration, new items were developed to investigate further issues of understanding. Both tests were used at different schools in the format of a cognitive interview; Test 1 was also used at another school as a written test. Additional items were developed to use with groups of teachers in an attempt to challenge early findings; these teacher trials used a third assessment format requiring both a written answer and a written explanation of method. In Test 1 students were assessed with pairs of items. In each pair one item used a decontextualised number line, the other a measurement or graphing context promoted by the curriculum. During the cognitive interviews, the verbal responses of students were recorded on audiotape, while field notes were used to capture non-verbal data. Follow-up probe questions were used to clarify solution strategies and the understanding underlying these strategies. The written test was then used to identify if the interpretations made could be transferred. Test 2 repeated the data collection methodology from Test 1 but used a different structure within the test. In total, 45 cognitive interviews and 81 written tests were undertaken with students, while 32 teachers participated in the teacher trials. Facilities, point bi-serial correlation coefficients, and levels of significance were used to ascertain the fitness for purpose of the developed test items. Data collected during the cognitive interviews were also analysed using both qualitative and quantitative methods to ascertain patterns of response. The mathematics curriculum in New Zealand had assumed that students would develop understanding about scale from exposure to scales in measurement and graphing situations. This approach might have been appropriate if a scale was a simple (or single) object to be mastered but it is not. A scale is a mathematical tool of vast flexibility that can be applied in numerous forms to a wide range of situations. The results suggest that teaching of scale needs to be more deliberate, and also needs to be considered when curricula are designed. A high proportion of the students in the study had not developed the expected understanding of scale by Years 7 and 8. A complex series of factors were identified that impacted on how the students worked with scale. These included: their understanding of number and number symbols; their understanding of the measurement conventions that are foundational to scale; the strategies they had developed to partition unmarked intervals; their strategies to decide on the value of a partition in marked intervals; their understanding of the role of the marks and spaces on the scale; and their ability to iterate a unit. These different bodies of understanding needed to be integrated and used in a coordinated manner for the students to become effective users of scale.</p>

Pathology of obstacles of implementation of national curriculum document of Iran from the perspective of curriculum professors

The aim of the present study is to identify the obstacles to the implementation of the National Curriculum Document of the Islamic Republic of Iran from the perspective of curriculum professors. 46 professors of public universities in Tehran were selected as the available statistical sample. The results of the study indicate that the average importance of obstacles to the implementation of this document is a significant difference between the sample average and the hypothetical average of the community at a significant level of 0.01 (t = 58.30). The results indicate that the importance of obstacles to the implementation of this document is moderate to high because the average obtained 3.72 is higher than the hypothetical average of number 3. Also the results of Friedman test show that from the perspective of respondents, the most important obstacle to the implementation of this document was the human obstacles, and the least important factor was structural obstacles. This relationship is also statistically confirmed because the significance level obtained is less than 0.05.

Pathology of obstacles of implementation of national curriculum document of Iran from the perspective of curriculum professors

The aim of the present study is to identify the obstacles to the implementation of the National Curriculum Document of the Islamic Republic of Iran from the perspective of curriculum professors. 46 professors of public universities in Tehran were selected as the available statistical sample. The results of the study indicate that the average importance of obstacles to the implementation of this document is a significant difference between the sample average and the hypothetical average of the community at a significant level of 0.01 (t = 58.30). The results indicate that the importance of obstacles to the implementation of this document is moderate to high because the average obtained 3.72 is higher than the hypothetical average of number 3. Also the results of Friedman test show that from the perspective of respondents, the most important obstacle to the implementation of this document was the human obstacles, and the least important factor was structural obstacles. This relationship is also statistically confirmed because the significance level obtained is less than 0.05.

UNMASKING THE EFFECTS OF TEACHERS WHISTLEBLOWING SOME ATTRIBUTES ON IMPLEMENTING STEM EDUCATION: NATIONAL CURRICULUM DOCUMENT 2006 PERSPECTIVE

Purpose of the study: The purpose of the current research was to measure the effect of teachers self-efficacy, locus of control, and emotional labour on implementing STEM education, focusing on national curriculum document 2006 concerns/guidelines. The researchers enthusiastically explored and reported actual situations happening to implement STEM Education in male public sector primary schools of district Lahore, Punjab province of Pakistan. Methodology: The researchers structured quantitative leading to ex post facto research focusing positivist paradigm on a sample randomly selected 530 participants. The researchers administered Henson (1999) Sources of Self-efficacy Inventory, Rose and Medway (1981) Locus of Control Scale, Çukur (2009) Teachers Emotional Labour Scale, Nistor et al. (2018) Teachers questionnaire on STEM Education Practices and self-constructed questionnaire on national curriculum document 2006 based concerns/guidelines on STEM Education, to collect the data from male primary schools teachers working in public sector schools of Lahore. The researchers run regression analysis and Pearson Product Moment Correlation (r) to analyze the data. Main findings: Findings of the current research revealed that teachers self-efficacy have affected 82.90%, locus of control 65.60%, emotional labour 70.50% and national curriculum document 2006 have affected 28.10% on implementing STEM education. Moreover, a significant strong relationship existed between self-efficacy and STEM education (r = .910**, n = 528, p < .05), locus of control and STEM education (r = .873**, n = 528, p < .05), emotional labour and STEM education (r = .840**, n = 528, p < .05) and a significant and weak association yield between national curriculum 2006 concerns and STEM education (r = .002**, n = 528, p < .05). Applications of the study: The findings of the current research will be applicable for primary schools male teachers who break the ice about their cognitional, social, and emotional attributes that are practised to implement STEM education focusing national curriculum document 2006; as they monotonously worked for students lap of luxury. Novelty/originality of this study: There are hardly any studies conducted on self-efficacy and STEM education but, void researches structured to measure the effect of teachers locus of control, emotional labour, and national curriculum document 2006 based concerns/guidelines on implementing STEM education. The authors has made a significant contribution by portraying clear pictures of current appealing situations happening in male public sector primary schools of district Lahore of Punjab-Pakistan.

Instances of Exclusion and Inclusion in Ontario's Grade 9/10 Canadian and World Studies Curriculum Document

This paper will evaluate the extent to which grade 9/10 Canadian and World Studies curriculum in Ontario perpetuates a monolithic, nation centered focus of citizenship and history at the exclusion of racialized and immigrant groups, and to what extent it includes racialized and immigrant groups. To achieve this, an anti-racist theoretical framework was utilized and the following themes obtained from the literature review were applied: Hegemony, citizenship education and global citizenship education, and curriculum design. Other sub-themes which have informed the broader categories mentioned above are racism and nationalism.

Instances of Exclusion and Inclusion in Ontario's Grade 9/10 Canadian and World Studies Curriculum Document

This paper will evaluate the extent to which grade 9/10 Canadian and World Studies curriculum in Ontario perpetuates a monolithic, nation centered focus of citizenship and history at the exclusion of racialized and immigrant groups, and to what extent it includes racialized and immigrant groups. To achieve this, an anti-racist theoretical framework was utilized and the following themes obtained from the literature review were applied: Hegemony, citizenship education and global citizenship education, and curriculum design. Other sub-themes which have informed the broader categories mentioned above are racism and nationalism.

Relationship between Teachers’ Professional Commitment and Formative Assessment Practices as a Part of Curriculum Implementation at Secondary Level in Punjab

National Curriculum for English in Pakistan, reveals its intentions for acquiring language related international requirements concerning with career choices and furthering education. Formative assessment is at the center of students’ learning and is devised in the curriculum document providing basis for its implementation. Curriculum implementation is pivotal to classroom practices of teachers. Curriculum guides teachers to implement formative assessment. Professional commitment contributes enriching teacher’ classroom practices. Focus of the study was to examine formative assessment practices of teachers, as a part of curriculum implementation, in accordance with curriculum document and its relationship with professional commitment of secondary school English teachers. Study secures its significance for teachers, curriculum developers, and governmental agencies. Quantitative survey was the method adopted for the study and explanatory correlational design was used. Teachers, concerned with teaching of English at secondary level, from entire secondary schools working under the supervision of the Punjab province were the study population. Sampling procedure employed multistage stratified random sampling technique and 576 teachers were selected as study sample. Two questionnaires were developed that included questionnaire regarding implementation of formative assessment (QIFA) and teachers’ professional commitment scale (TPCS). Survey was conducted as a data collection strategy. In statistics, Mean and Spearman correlation were employed. Results revealed that professional commitment of teachers and their formative assessment practices were moderate. Results regarding relationship between the variables; professional commitment of teachers and their formative assessment practices were significant correlated. The study recommended school based teacher trainings to sensitize and enhance teachers’ awareness and practices towards formative assessment practices as a part of implementation process. Governmental agencies are needed to focus the situation of professional commitment of teachers and implementation of formative assessment as a part of implementation.

The development of a curriculum for the introduction to trade show buying

This study addresses the need for the development (design, implementation, and evaluation) of an accurate and useful curriculum targeted at educating current and future businesspersons contemplating the procurement of merchandise or services through trade shows. In the field of business education, the procurement of products to be sold is an important component of the marketing curriculum. One source for product procurement is trade shows. However, trade show buying has not been adequately addressed within current marketing curricula.<br/> Expert panels were utilised to evaluate the curriculum as it was developed. One expert panel was made up of current trade show buyers; another panel was composed of trade show vendors; and another panel was composed of academic/business education experts related to marketing and continuing education. The curriculum was evaluated by the expert panels for both accuracy and usefulness. The actual curriculum document was designed as a user-friendly quick reference guide for new and/or experienced trade show buying practitioners. Although this study largely addresses organisational buyers, they are also customers and this study into their behaviour may also provide insights into customer buying behavior in general.

An Analysis of Pakistan’s National Curriculum of Mathematics at Secondary level

The purpose of the study were to analyze the Curriculum document of National Curriculum of mathematics of secondary grades. The study employed qualitative research paradigm within it the discourse analysis technique was used to analyze the mathematics curriculum document. Discourse analysis helps in understanding the written, spoken and signs language used in any document analysis. The sample of the study were foreword, introduction, objectives, reviewer’s notes and list of reviewers, the sections of mathematics in the national curriculum of mathematics (2006) for secondary grades. The findings of the study revealed that the National Curriculum of mathematics (NCM) 2006 was focused on transfer of Knowledge. However, it neglected the conceptual understanding of essential subject matter. It has been also discovered that the content of the mathematics is not taught according to the prescribed curriculum. Moreover, standard were not implemented properly. The role learners were recipient of knowledge and that of teachers is transmitter .Thus, it neglected the participatory and constructive approach of teaching and learning mathematics. Moreover, the curriculum ideology was not considered while developing the mathematics curriculum. It is suggested that the curriculum developers should revisit the policy on social constructive approach so that curriculum can be taught conceptually rather than standard based. Moreover, formative assessment should be included throughout the year rather taking annual examinations. It is recommended that teachers should impart mathematics education by linking math to social context and encourage students to construct meanings socially.