Secondary Level Mathematics Research Articles

Teachers' Perceptions of Assessment in Mathematics as Students at Secondary Level

This paper focuses on my study of a narrative research inquiry and interpretative paradigm under a qualitative research approach of in-service secondary level mathematics teacher of Kavrepalanchok district in Nepal based on my research. The study included five in-service teachers from the district chosen using a purposive sampling strategy. As a data collection strategy, I conducted in-depth interviews utilizing interview guidelines to elicit the narrative stories of response participants. I used qualitative data analysis methods to transcribe the participants' shared tales in order to generate themes. I gained the insight that absolutism and positivistic notions of mathematics education had influenced assessment practices in Nepal fifteen years ago from 2005 AD to 2020 AD. At the time, constructionist education for creating mathematical knowledge through assessment was uncommon. To enable mathematical learning, the students had fewer possibilities for competition-based learning, engagement, communication, and teamwork. Furthermore, the curriculum design of secondary level mathematics at that time was exclusive to focus on students' need, interests, and individual learning capacities Instead, math teachers took mathematics as a subject for gifted children and did not focus enough attention on individualized education for low-performing students. Students learned mathematics designed with a disengaged curriculum, non-participatory teaching, and insufficient evaluation using technology. Mathematics teachers did not frequently choose to develop a questioning environment in the classroom as part of the students' assessment. By focusing on summative assessment and paper pencil tests as a typical assessment approach, teachers overlooked student variety. Students lacked motivation, feedback, and encouragement from teachers when it came to assessment, which resulted in poor academic performance. Because the mathematics textbooks were published in English, students frequently had issues with the medium of instruction, particularly at the plus two (+2) level or equivalent to the intermediate level.

Behavioral, cognitive, emotional and social engagement in mathematics learning during COVID-19 pandemic.

A meaningful engagement of learners is critical in the quality teaching and learning of mathematics at school level. Learner engagement has been an ongoing issue in mathematics classrooms in Nepal and elsewhere. In this context, this study aimed to examine the level of engagement (behavioral, social, emotional, and cognitive activities) and their association with learning mathematics through the virtual mode of instruction during the pandemic. The cross-sectional online survey design was employed among 402 secondary-level mathematics teachers in Nepal. Descriptive statistics, correlation, and structural equation modeling were the major statistical techniques used in research. The findings indicate that the level of behavioral, social, emotional, and cognitive engagement of students was found to be high in the online mode of instruction. Additionally, cognitive engagement has significant highest impact on social, behavior, and emotional engagement.

Instrument for evaluating historical resources in mathematics textbooks

The article describes an instrument consisting of 46 indicators organised under 10 dimensions to assess the presence and educational utility of historical resources in secondary education mathematics textbooks. The instrument was constructed on the basis of previous research on the didactic use of the history of mathematics, existing instruments on the analysis of mathematics textbooks, and mathematics teachers’ assessments of the suitability of the indicators. The instrument can be used as a stand-alone tool or integrated into other procedures addressing textbook analysis more broadly. Its application is illustrated with a sample comparison of two secondary level mathematics textbooks. The instrument has proven to be a useful tool for comparing the historical resources in different publishers’ textbooks, for it enables secondary school mathematics teachers to base their choice of resources on an appraisal of the indicators most relevant to classroom teaching.

TEACHERS’ AWARENESS OF MATHEMATICAL APPLICATIONS IN DAILY LIFE

The goal of this research was to look into the current state of Secondary level Mathematics teachers’ awareness of the use of mathematics in daily life in the State of Telangana. In this present study the investigator identified the awareness in use of mathematics in daily life is in eight areas such as Mathematics awareness in Environment, Science and Technology, Agriculture, Art and Culture, Sports, Weather Forecasting, Industry. The researcher used a mailed questionnaire to collect data for his research for Secondary level Mathematics teachers’ awareness in use of mathematics in daily life in selected areas. The study revealed that secondary level mathematics teachers have good awareness in use of mathematics in daily life. Over 80 percent of Secondary level Mathematics teachers’ in this study were using daily life situations to understand the concepts and gain the fundamental knowledge of other subjects such as Environment, Science and Technology, Agriculture, Art and Culture, Sports, Weather Forecasting, Industry among the students.

Teachers' Practices of Assessment in Secondary Level Mathematics

The purpose of my study was to find teachers' practices of assessment in mathematics at secondary level from 2005 AD to 2020 AD in the local context in Nepal. I conducted the study in Kavrepalanchok district in Nepal with a narrative research inquiry and interpretive paradigm under a qualitative research approach. The construction of assessment knowledge by in-service mathematics teachers as participants was the epistemology of my research, which tried to explain subjective perception through mental constructs. Interactions and communication among students contribute to the construction of reality.
 I conducted in-depth interviews using interview guidelines to excavate the narrative stories of respondent participants as a method of data collection. I transcribed the shared stories of the participants to generate themes using qualitative tools of data analysis. Five in-service teachers selected using a purposive sampling method from the district were the participants in the study.
 In-service mathematics teachers in Nepal are passionate about instilling curiosity and motivation in their students, and they are particularly interested in contextual assessment related to their daily activities. Sufficient feedback from the mathematics teachers has supported students to promote their mathematics learning. The study concluded that mathematics assessment practices provide multiple opportunities for teachers and students to transform their usual practices and establish classroom activities as a discourse for knowledge construction.

Challenges Encountered by Mathematics Teachers in ICTs Implementation

Information and communication technologies (ICT) have a great deal with teaching and learning processes to conceptualize abstract concepts in mathematics. The objective of this study investigated the challenges encountered by secondary-level mathematics teachers while implementing ICT-based training in a classroom in teaching. We used interpretive inquiry as an approach to research. As the study tools, we used in-depth interviews, observations, and generated textual data. We analyzed the data by adopting the data's sequential coding, categorizing, and thematizing. We used constructivism as a theoretical lens to understand and explore the use of ICTs. We envisaged and generated the themes on challenges that are inadequate ICT-based professional development training and tools; lack of competency in technological/ pedagogical content knowledge; disempowering school actors; enduring 'one size fits for all'; structured curriculum; lack of infrastructure and ICT tools and hegemony of traditional classroom practices. The significance of the use of ICTs has been recognized in public schools in Nepal. There was also evidence that the current practice of ICT-based teacher education and development was not excess in developing skills and knowledge to use ICT in their classroom.

Teachers' Mindset on Gender Responsive Pedagogy (GRP) in Mathematics Classroom

The purpose of this study was to analyze mathematics teachers' mindset regarding GRP practices in their classroom set up and classroom activity at secondary school level. The respondents were 120 mathematics teachers (106 male, 14 female), who were teaching mathematics at grade IX and X and were selected randomly. The participants were from three districts: Kathmandu, Sindhuli, and Chitwan of Province Three of Nepal. Cross-sectional Survey design was employed for this study. Self- developed questionnaire was considered as the data collection tool. The collected data were analyzed using descriptive statistics (Mean and Standard Deviation) and inferential statistics (One Sample t-test). The result of the study indicated that secondary level mathematics teachers are practicing GRP on classroom set up and classroom activity. However, they did not give more time and effort for girls for learning mathematics and low practice of group work for cooperative learning, which is important for reducing gender bias and empower girls in learning mathematics. The Government of Nepal should provide teachers GRP awareness training about how to practice GRP in classroom through policy and changing concept in school curriculum and promote positive mindset towards GRP practice.

Teachers’ motivational profiles and their longitudinal associations with teaching quality

This study used an integrated theoretical approach to investigate teacher motivation and its influence on teaching quality. Drawing on Expectancy-Value-Theory and Achievement-Goal-Theory, a person-centered approach was used to investigate how multiple characteristics (i.e., self-efficacy, enthusiasm, and goal orientation) combined to form teachers’ motivational profiles. The profiles were then analyzed to see if there was a link to teaching quality. Latent profile analysis for 156 secondary-level mathematics teachers identified three motivational profiles which differed only in their performance goals: low performance goal-oriented (49%), high performance goal-oriented (38%), and high performance-avoidance goal-oriented (13%). Multilevel path analysis showed that motivational profile membership was not significantly related to student-rated teaching quality when baseline teaching quality was controlled (N = 1497 available on both measurement points). The findings revealed that the link between teacher motivation and teaching quality was less clear than expected. Possible reasons for the results are discussed.

How Do Pre-service Mathematics Teachers Enhance Their Lessons through Lesson Study?

This study aimed to investigate how lesson study perspective could help pre-service teachers (PSTs) to enhance their mathematical instruction. Four PSTs along with their 13 other peers who took a semester long secondary level mathematics teaching methods course in one of the large-midwestern universities in the US participated in this study. While four PSTs planned and taught a lesson in two different groups by two, other PSTs took the role of giving feedback to their classmates. PSTs enhanced their lesson plans based on the feedback from their peers and provided self-reflections on these changes. As a result of the investigation of the changes PSTs did on their lesson plans and the reflections they provided, it was revealed that they enhanced their instruction on some specific issues, such as getting students’ attention, using time efficiently, maintaining student interaction, using technology. It is also suggested to future researchers that it would be beneficial to study on PSTs’ assumptions on the difference between the real students and the PSTs who pretended as students during the peer-taught lesson study activity.

Mathematical modeling of tech-related real-world problems for secondary school-level mathematics

The use of authentic real-world problems that reflect the applied nature of mathematics is not prevalent in formal secondary school settings. In this study, we explore the interface between workplace mathematics, particularly tech-related real-world (TRW) problems, and school mathematics, through the explication of mathematical modeling. The research questions are (1) in which tech domains can real-world problems be identified that can be addressed using mathematical modeling for the secondary school level? (2) Which methods do engineers use to simplify tech-related problems for non-experts in their field? (3) In which areas in the secondary mathematics curriculum can TRW problems be mapped? We present a three-phase model which yielded the creation of a pool of 169 TRW problems. The first two phases of the model included extracting authentic problems from the work of tech engineers and simplifying them to be meaningful or perceivable to students. These were explored by conducting task-oriented interviews with senior tech engineers and scientists from leading companies and universities. The third phase was accomplished by interviewing mathematics education experts, and included verifying the compatibility of the problems with the formal, secondary-level mathematics curriculum. The study has methodological, theoretical, and practical contributions. These include methodology that enables identifying TRW problems that are compliant with the secondary mathematics curriculum; adding to the literature about mathematical modeling by demonstrating the interface between workplace mathematics and school mathematics; and creating a large pool of TRW problems that can be used in secondary school math lessons.

Effectiveness of GeoGebra in teaching school mathematics

This article aims to explain the effectiveness of using Information and Communication Technology (ICT) in teaching and learning school mathematics. The paper is based on the results of one month experiment of Geo Gebra software in teaching and learning the concepts and problems included in the chapter commensuration of secondary level mathematics. The effectiveness of using ICT tools were explored by measuring achievement level with the help of achievement test and overall perceptions of using ICT tools through questionnaire. The data were analyzed and interpreted by using table, frequency, percentage, mean, SD and t-test. The findings revealed that there was high mean score in achievement in mathematics of experimental group (teaching with ICT) than that of control group (without using ICT), and the difference was significant at 0.05 level. Likewise, the students of experimental group had positive perception to support the use of ICT tools in teaching and learning mathematics. Thus, the use of ICT, particularly Geo Gebra is an effective tool to increase achievement; to promote curiosity, creativity; to make clear sense of concepts; and to encourage overall learning of students in mathematics. Finally, the study suggests that school mathematics teachers need to use ICT for effective teaching and learning.

Implementation of STEM in Secondary Mathematics Classrooms: Identification of Teachers' Beliefs

The purpose of this study was to investigate teachers’ beliefs about the implementation of STEM (Science Technology Engineering and Mathematics) approach in secondary (6-12 grades) mathematics classes and identify intervening belief aspects. A questionnaire was developed regarding practicing secondary level mathematics teachers’ beliefs about the implementation of STEM in mathematics classes. An online form of the questionnaire was created and sent to all secondary math teachers in two counties in the state of Florida. Eighty-two were received back from teachers. The results of factor analysis confirmed that items were distributed under five major aspects. Finally, the results of the data analysis disclosed that although most teachers believe that the implementation of STEM education is necessary, some have concerns about the effectiveness of the implementation because of shortages of materials, resources, and equipment needed for implementation of STEM. Another important finding is that teachers don’t have appropriate and sufficient knowledge for the implementation of STEM activities.

Numeracy and migrant students: a case study of secondary level mathematics education in Norway

Previous research has shown that adults from migrant backgrounds often have lower numeracy competence than do their majority counterparts, even though many were educated in their host country. Leaving secondary education with lower levels of numeracy competence than majority students potentially makes migrant students vulnerable as adults, as the lack of numeracy competence can negatively impact their opportunities to participate in work-life and society, in addition to affecting their everyday lives. Thus, it is vitally important to understand how mathematics education at the compulsory level can offer migrant students opportunities to develop numeracy competence. This paper presents a case study of four Norwegian lower secondary mathematics teachers. These teachers were asked to reflect on their classroom practices and on how they adapt teaching and assessment situations to migrant students. Our findings show that the teachers valued diversity in their classrooms and that their teaching was student-centred, focused on assessment for learning and problem-solving practices. These are potential building blocks for culturally responsive teaching. However, the teachers mainly focused on language issues, while cultural aspects of classroom participation and mathematical activity were neglected. This paper argues that such views may potentially hinder the provision of equal opportunities for all students to become numerate and, therefore, may contribute to maintaining migrant students—and the migrant adults they will become—as a vulnerable group.

Empowering the Disadvantaged Students in Mathematics Education: Relevance of Social Justice, Equity and Mainstreaming

Mathematical knowledge is indubitable in various sectors, but diversity in culture and tradition in society causes inequality, injustice and backwardness among the students learning mathematics. Study of cultural heritage, customs, behavior in mathematics education is the demand of post-modern paradigm. Efforts of self-organization and co-construction in the initiation of students and teachers through their active participation, interaction and mathematics classroom discourses could be instrumental towards the generation of mathematical knowledge in classroom – which can support to reduce the western domination in mathematics education; and societal negative mind-set about mathematics education will also be minimized in this way. Ethno-mathematics, diversified mathematical strategies, culturally responsive mathematics classroom and enhancing equity in learning mathematics are the major dimensions that mathematics professionals need to exercise for the effective, reflective and contextualized teaching and learning of mathematics. This is a phenomenological study conducted among secondary level mathematics teachers. Using written interview and informal sharing of participants’ experiences towards teaching and learning mathematics, three major themes were developed and discussed. This article primarily shows that there exists the intertwined relation among these themes; and it is essential to properly address these themes for more effective learning of mathematics in the context of Nepalese secondary level classrooms.

Primary Teacher’s Expectation with their Children to Make Senior Teacher

Teacher can have different expection with their children to make senior in the future. This study aimed to explore primary level teachers’ expectation with their children to make secondary level mathematics teachers. A phenomenological study was conducted with primary teachers. Three public schools, one from each of Dhading, Gorkha and Kavrepalanchock district were selected conveniently. Three primary teachers respondents, one from each sample school were selected purposively. A semi-structured interview was the main method of data collection. The thematic analysis showed that primary level teachers have a common motivation of teaching their children mathematics and to make them secondary level mathematics teacher in future due to their bitter experiences of being a junior, the judgment of society toward them and leading their children a worthy life fulfilling their dreams. Further earning through tuition and other extra classes and the prestigious job is the other motivating factor to make their children secondary level mathematics teacher which brings prosperity and happiness in their life and family.

Appraising Adequacy of Standard Based Curriculum 2006 and Allied Secondary School Mathematics Textbooks for Higher Order Thinking Skills (HOTS) in the Punjab, Pakistan

In Pakistan the curriculum was revised in 2005-06 and corresponding textbooks for secondary school mathematics were developed and adopted for session 2012-13. This study was conducted to analyze the adequacy of the curriculum and the newly adopted textbooks in instilling the HOTS in students. The research design used was descriptive in which data was analyzed both by qualitative and quantitative methods. Web Alignment Tool was used to assign Depth of knowledge (DOK) levels to the prescribed students learning outcomes (SLOs) for secondary level mathematics in Pakistan. The outcomes of the study show that the curriculum is predominated by the SLOs of DOK level 1(204 out 280 SLOs). There is no SLO of DOK level 4. There are 70 SLOs of DOK level 2 and only six SLOs of DOK level 3. The entire format of the textbooks is monotonous as it mostly guides the students to learn an algorithm to deal with any SLO. This is followed by an exercise of sums to practice the learnt algorithm without any appropriate learning experience. It is suggested to revise the respective curriculum by adopting fewer, higher and deeper approach. For DOK level 2 and above, appropriate learning experiences should be incorporated in the curriculum and textbooks.

Fraction interventions for struggling elementary math learners: A review of the literature

AbstractUnderstanding fractions has been a pervasively difficult skill for struggling math learners, yet it is essential for success in secondary level mathematics skills. The present systematic review examined the evidence base of fraction interventions for elementary level students identified as struggling math learners. Twelve studies met inclusion criteria and were reviewed for (a) instructional focus (b) instructional components, and (c) effectiveness of the intervention on fraction performance. The majority of studies had a primary instructional focus on conceptual knowledge of fraction learning. Results of the study also indicated that all interventions included multiple evidence‐based instructional components (e.g., concrete and visual representations, range and sequence of examples, etc.). These multicomponent interventions improved performance on a variety of proximal fraction outcome measures. Intervention effects were mixed for generalized outcome measures and minimal for distal outcome measures. Limitations, implications for practice, and future research directions are discussed.

Using Grounded Theory to Extend Existing PCK Framework at the Secondary Level

This paper addresses two critical issues in mathematics education, the need: (a) to understand the nature of educator’s subject matter knowledge and pedagogical content knowledge; and (b) to find ways to measure them. It stems from a mixed-methods study designed to inspect the secondary mathematics teachers’ pedagogical content knowledge (PCK) related to the area of a trapezoid, a common topic in intermediate/secondary school classes. Based on the provided exemplars of student work, in-service teachers were invited to propose possible ways for addressing perceived difficulties of students and provide extensions. Using a Grounded Theory approach, we identified themes in our data and incorporated them with existing conceptualizations of knowledge for teaching secondary level mathematics, and developed rubrics that allow discriminating different levels of teachers’ PCK. In this paper, we describe the process of developing the rubrics, and propose ways to: (a) extend the existing frameworks for PCK in/for teaching mathematics at the secondary level; and (b) measure multiple facets of PCK in order to design technology-based professional development for mathematics teachers.

Longitudinal relations between teaching-related motivations and student-reported teaching quality

Teaching-related motivations are often assumed to influence teaching quality; however, the empirical evidence regarding the directionality of such influences is scarce. The present study thus examined the reciprocal links between teaching-related motivations (self-efficacy and enthusiasm for teaching) and student-reported teaching quality (classroom management, learning support, and cognitive activation). Two-level cross-lagged panel analyses across three time points (with an initial sample of 165 secondary-level mathematics teachers and their 4273 students) revealed no significant cross-lagged effects when teachers' stable inter-individual differences are taken into account. Our findings suggest that teachers' motivations are remarkably stable over time.

Comparing episodes of mathematics teaching for higher achievers in England and Germany

To illustrate similarities and differences in lower secondary level mathematics teaching with higher achievers and thereby explore privileging processes, we contrast a teaching episode in Baden-Württemberg, Germany with one in South West England. These have been selected from a larger study as typical within each region for higher achieving students in the school year in which they become 12 years old. These episodes reflect the dominant discourses and recent policy initiatives in each country. Descriptions of the episodes are linked to wider debates about the ways education practices benefit some student groups, and potential areas for further exploration are identified.