Secondary Mathematics Classes Research Articles

Marching to the Beat of One’s Own Drum: A Comparison of Students’ Understanding of Linear Equations and Perspectives on Learning Mathematics in a Flipped and Non-Flipped Classroom

This study compared two teaching approaches (flipped vs non-flipped) for the topic of linear equations in two Australian secondary mathematics classes taught by one teacher. Both the flipped and non-flipped classes demonstrated similar improvement in understanding directly after the topic. However, the flipped class had greater retention of understanding three weeks after the topic. Student attitude data showed no significant differences (p > .05) between the two classes before or after the topic. Open-ended responses from students revealed favorable perceptions of the flipped approach for most students. These included enhanced support for learning through an ability to control their own learning and ability to review explanations on demand. Some students expressed difficulty in not being able to seek immediate clarification from the teacher when watching the videos, highlighting a drawback of the approach.

Supporting self-regulated learning in a secondary applied mathematics course

<p>This study examines how one teacher supported low-achieving students’ self-regulated learning (SRL) in the context of a secondary mathematics class. The teacher’s scaffolding provided students with multiple opportunities to use feedback and adapt learning and study strategies. Data compared pre- and postmeasures of metacognitive skills, motivational beliefs, and learning and study behaviours, and examined the effects of directed practice on students’ developing SRL as well as their mathematics achievement. Results suggest the need for more research into the effects of individualized, targeted supports, particularly in assisting students in using metacognitive feedback to adapt learning strategies.</p>

The Effects of Mobile Technology on Learning Performance and Motivation in Mathematics Education.

Due to rapid developments, mobile technologies started to play an essential role in designing seamless learning environments. Due to the availability of mobile technologies, students can access learning materials without being bound by time and place. On the grounds that these applications allow information exchange, time and space limitations such as classrooms or school bells have been eliminated. Therefore, this study aims to assess mobile-assisted seamless learning environments’ effects on students’ success and motivation in the secondary school 7th grade mathematics class algebra unit and student opinions about the application. The research is designed using the descriptive pattern of mixed-method research. The sample of the study is 73 middle school students (30 male and 43 female) in Turkey. Augmented Reality (AR) applications developed in teaching algebra to support individual learning and to utilize mobile technologies, WhatsApp groups were created. Algebra Achievement Test (AAT), Mathematics Motivation Scale (MMS), and semi-structured interview forms were used as data collection tools in the research. The results of the study showed that there were statistically significant differences in favor of the experiment group in AAT and MMS scores. However, no significant difference was found between the groups in intrinsic goal orientation and test anxiety scores, which are motivation sub-dimensions. The findings obtained from AAT, MMS, and the students’ opinions showed that mobile technology applications used in out-of-school learning environments positively affect the learning process.

"We are much closer here": exploring the use of WhatsApp as a learning environment in a secondary school mathematics class.

In this study, we examined a mathematics teacher’s communicative acts on an instant messaging tool, WhatsApp, and its role in creating a sustained learning environment between secondary-school students and a teacher in Turkey. The interactions of a mathematics teacher and his students (n = 38) over two years were explored. The WhatsApp group increased interaction in out-of-school hours. Analysis of the teacher’s communicative acts was the leading force that encouraged the group to continue to interact. The teacher portrayed an informal and sincere presentation of himself on social media. A constructive communication style between teacher and students was fostered by connecting through WhatsApp in out-of-school hours, when the teacher’s informal communicative acts have facilitated their learning.

The integration of faith, culture and life in Catholic schools: keys to understanding and pedagogical orientations

This paper discusses the integration of faith, culture and life in Catholic schools, offering keys to understanding and pedagogical orientations. First, based on magisterial documents, the text identifies three features that characterise this integration: a comprehensive understanding of knowledge, a testimony offered through the lives of teachers, and an approach to Catholic schools as a ‘community laboratory’. Second, the paper exemplifies the integration of faith, culture and life through a secondary school mathematics class. This example allows manifesting those three features in concrete pedagogical practice. Finally, the paper provides orientations that can foster the integration of faith, culture and life in Catholic Schools. These guidelines are related to: promoting teaching-learning experiences based on analogy, discussing the understanding of knowledge that runs through the school curriculum, articulating the pedagogical principles that guide teachers’ work, and guaranteeing institutional commitment to transform the school into a community laboratory.

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.

Social climate and help-seeking avoidance in secondary mathematics classes

In Australia, student under-participation and disengagement in secondary mathematics classes are persistent problems. Academic help seeking is a unique self-regulated behaviour that is important for engagement in mathematics classes and yet many students avoid seeking help from teachers and peers as they progress through secondary school. The aim of this study was to explore the relationship between students’ perceptions of the social climate of their classrooms and their avoidance of help seeking in secondary mathematics classes. Students’ perceptions of classroom social climate, along with perceptions of their own academic and social self-efficacy, self-theories of intelligence, and help-seeking goals and intentions, were assessed for a sample of 551 Australian students in 47 classes from eight secondary schools and two vocational institutes. The measurement model for social climate was reduced to four factors (Task Orientation, Teacher Support, Cooperation and Investigation) and a mediated structural equation model, informed by theory and previous empirical studies, was assessed using Mplus. Bootstrap confidence intervals were used to assess the direct and indirect effects of social climate on help-seeking avoidance. Findings indicated that Task Orientation and Cooperation had a negative effect on help-seeking avoidance, while Investigation had a positive effect. Teacher Support was not associated with help-seeking avoidance. Implications for practice are discussed.

Self-determination theory and the flipped classroom: a case study of a senior secondary mathematics class

Teaching senior secondary mathematics presents a number of challenges, such as provision of a prescribed curriculum, homework expectations and preparing students for externally imposed high-stakes assessment tasks. In order to address these challenges, an increasing number of senior secondary mathematics teachers are incorporating a flipped classroom approach into their teaching. While enactments of the approach vary, it typically involves delegating the more routine instructional mathematical content as homework videos, allowing for more targeted in-class teaching. Traditionally in the domain of tertiary teaching, it is becoming more common in secondary school settings and seems to address students’ needs for competence, autonomy and relatedness, which comprise self-determination theory (SDT). This paper looks at a case study undertaken with an Australian grade 12 class where the teacher utilised a flipped classroom approach to teach mathematics 2. Data were collected through an online survey, interviews and classroom observations. The results showed that SDT was an appropriate lens to analyse participants’ experiences of the approach, with the teacher being a particularly strong influence on students’ motivation for engaging with the approach. The study adds to the limited literature on examining enactments of the flipped classroom in senior secondary mathematics contexts and has implications for practice in terms of identifying the practices and factors which influence students’ motivations for engaging in mathematics classes.

Enhancing Secondary Students’ Goal Attainment and Self-Determination in General Education Mathematics Classes Using the Self-Determined Learning Model of Instruction

Almost every state includes content standards that are closely related to skills associated with self-determination (e.g., decision making, planning, problem solving, goal setting and attainment). Additionally, research in both general and special education has demonstrated a close relationship between the promotion of self-determination and positive school (e.g., academic goal attainment) and post-school (e.g., employment) outcomes. Therefore, this study examines implementation of an evidence-based intervention to promote self-determination in inclusive, general education classrooms. This study utilized multilevel linear modeling to examine changes in student self-determination in secondary mathematics classes after a year of exposure to The Self-Determined Learning Model of Instruction (SDLMI). Participants included were 81 students ranging from 10th to 12th grade learning in secondary mathematics classes (Algebra II, Pre-Calculus, and Advanced Placement Calculus). The findings demonstrated a small, positive effect on student self-determination and that goal attainment during the first semester predicted second semester goal attainment. Specifically, the inclusion of goal attainment as a predictor explained 10% of the variability in self-determination observed, corresponding to a small effect. Overall, students who attained at higher level of goal attainment had higher self-determination at the conclusion of the study and were expected to grow in their self-determination at a higher rate than those with lower levels of goal attainment. The results from this study suggest that implementing the SDLMI to support all students in secondary mathematics classes positively impacts student attainment of skills that impact self-determination and has the potential to impact mathematical learning in future research.

Changing students’ beliefs about the relevance of mathematics in an advanced secondary mathematics class

ABSTRACTThis study shows that using authentic contexts for learning differential equations in a differentiation-by-interest setting can enhance students’ beliefs about the relevance of mathematics. The students in this study were studying advanced mathematics (wiskunde D) at upper secondary school in the Netherlands. These students are often not aware of the relevance of the mathematics they have to learn in school. More insights into the application of mathematics in other sciences can be beneficial for these students in terms of preparation for their future study and career. A course differentiating by student interest with new context-rich curriculum materials was developed in order to enhance students’ beliefs about the relevance of mathematics. The intervention aimed at teaching differential equations through guided small-group tasks in scientific, medical or economical contexts. The results show that students’ beliefs about the relevance of mathematics improved, and they appreciated experiencing how the mathematics was applied in real-life situations.

Development of an Interactive Module Incorporating Financial Literacy in Teaching Decimals/Fraction

This study sought to develop an interactive module incorporating financial literacy in teaching fraction and decimals for Grade 7 Mathematics. This study used pretest-posttest one-group design with qualitative support to distinguish the effect of the interactive module on students conceptual understanding, financial literacy and motivation to achieve. Based on the quantitative and qualitative analyses of the study, there was a significant improvement in the students’ pre-test and post-test scores on conceptual understanding, financial literacy and motivation to achieve. Results also showed that students were able to understanding the concept of fractions and decimals; see application of fraction and decimals into different fields and most specially its connection to financial literacy. In addition, students realized the importance of savings and budgeting, and even became financially wise. The developed interactive modules incorporating financial literacy were integrated with interactive websites, financial literacy videos, and online assessments. The researcher recommends the use of the interactive module incorporating financial literacy in secondary mathematics classes to facilitate the learning process in teaching fractions and decimals. Also, similar interactive modules incorporating any real life skills must be developed.

Comparison of teacher and student perceptions of formative assessment feedback practices and association with individual student characteristics

This study (1) investigated similarities and differences in feedback perceptions among teachers and students and (2) explored the association between individual student characteristics and students' feedback perceptions. Survey data were collected from 59 teachers and 186 students in secondary English and mathematics classes in five Australian schools. Feedback quality was perceived more positively by teachers than students, and English teachers reported higher levels of facilitation of feedback use than students. Student self-reported levels of self-efficacy, intrinsic values and self-regulation predicted students’ perceptions of feedback quality. These individual student characteristics mediated the relationship between student achievement levels and feedback quality perceptions.

Deictics and the construction of mathematics and science knowledge in the secondary school classroom

Taking a Teacher Language Awareness (TLA) perspective, this paper examines how the concept of deixis is employed in oral discourse in two secondary science and mathematics classes in the southwestern part of the US. Drawing on audio and videotaped data from two classrooms, we examine how verbal deixis, or words and phrases that cannot be fully understood without additional context, serves as a potential resource for the organisation of learning processes. We further consider how deixis may act as an impediment to the organisation of learning processes. We outline implications for preparation of teachers of English Language Learners in Science, Technology, Engineering and Mathematics areas, with a specific focus on middle and high school science and mathematics.

The Didactical Contract Surrounding CAS when Changing Teachers in the Classroom

The article discusses three empirical examples of Computer Algebra System (CAS) use in Danish upper secondary school mathematics class with a recent change of teacher. All examples lead to didactical problems surrounding the situation and unclear expectations between teacher and students, involving loss of students’ mathematical skills and confidence, loss of global mathematical perspective, and the students losing sight of the mathematical objects in question. The article is the result of collaboration between two mathematics education researchers and an upper secondary school mathematics teacher, who experienced severe difficulties when taking over a class from another teacher. CAS was experienced as a crucial part of and reason for these difficulties. As a means for investigating the potential reasons behind the difficulties, a selection of constructs from the Theory of Didactical Situations (TDS) is applied. In particular, it is observed that unclear contractual relations about the role of CAS bring with them misguided winning strategies and metacognitive shifts, eventually causing the students to ‘lose the game’.

Belongingness and Pedagogy

In the present study, school belongingness was explored in the context of a mathematics classroom over the course of one academic year. In-depth interviews with eight African American middle school students and their three White teachers were conducted at two time periods. This phenomenological qualitative investigation of African American middle school girls revealed two primary themes of personal connection with their teachers and authentic pedagogy. As practitioners and researchers continue to examine the factors related to African American student achievement, empirical research should highlight the importance of teacher warmth and instructional relevance in the experiences of students of color in middle grades and secondary mathematics classes.

Rubrics in a Secondary Mathematics Class

Rubrics in a Secondary Mathematics Class

VADOVĖLIŲ NAUDOJIMO MOKANT MATEMATIKOS ANALIZĖ: ESTIJOS ATVEJIS

Associated Professor of Mathematics EducationTallinn UniversityAddress: Narva road 2510120 Tallinn, EstoniaE-mail address: mlepik@tlu.eeStraipsnyje pateikiama matematikos vadovėlių nau­dojimo mokant matematikos Estijos mokyklose analizė. Tradiciškai vadovėliai labai svarbūs mo­kant matematikos, tačiau šiandien vadovėlis nėra vienintelė matematikos mokymosi priemonė, mo­kytojas gali rinktis ir kitas priemones. Tarptautiniai TIMMS tyrimai rodo, kad efektyvus matematikos vadovėlių naudojimas pagrindinio ugdymo mokykloje daro įtaką mokinių matematikos mokymosi re­zultatams. Tai taip pat patvirtina įvairių šalių moks­lininkų atliekami tyrimai, kurie rodo, kad šiuolai­kiniai mokytojai labai įvairiai panaudoja vadovėlių medžiagą ugdymo procese. Straipsnyje pateikiami ir aptariami atliktos matematikos mokytojų apklausos (N = 164) ir pa­grindinės mokyklos ugdymo pakopoje stebėtų 29 matematikos pamokų tyrimų rezultatai, kurie pa­rodo, kokiais būdais Estijos matematikos mokytojai naudoja matematikos vadovėlius. Tyrimo duomenys rodo, kad vadovėliai nėra efektyviai panaudojami, neišnaudojamos visos vadovėlių galimybės, nors pusė aktyvaus pamokos laiko yra skiriama dirbti su vadovėliu. Tyrimo rezultatai atskleidė, kad dauguma mokytojų vadovėlį naudoja pratyboms, matemati­niams uždaviniams spręsti.

Authentic Argumentation With Prospective Secondary Teachers: The Case of 0.999…

Engaging prospective secondary teachers in mathematical argumentation is important, so that they can begin to learn to engage their own students in creating and critiquing arguments. Often, when we attempt to engage prospective secondary teachers in argumentation around topics from secondary mathematics classes, the argumentation is not authentic, as they believe they already know the answers. I suggest that there are problems related to the secondary curriculum around which we can engage students in authentic argumentation, and I propose one of them is whether 0.999… = 1. Purposefully engaging and supporting students in discussing this problem, and others like it, can lead to productive discussions that go beyond the answer to the question, including, for instance, what counts as evidence in mathematics.

Teachers’ Enactment of Content Literacy Strategies in Secondary Science and Mathematics Classes

AbstractThe incorporation of literacy strategies into content area instruction has been proposed as an effective way of improving student learning in the content areas. However, few studies have examined how teachers incorporate content literacy strategies into their instruction and the specific nature of implementation. As part of an ongoing professional development project on content literacy in secondary science and mathematics classes, we conducted a qualitative inquiry which examined the nature of teachers’ enactment of specific content literacy strategies through the analysis of classroom observations, teacher lesson plans, and teachers’ online discussions. Results show that teachers were using content literacy strategies; however, the nature of their enactment of these strategies varied in ways that influenced the learning outcomes. In this paper we describe a framework for characterizing these differences in enactment, provide examples of these variations, and discuss implications for enacting literacy strategies in these different ways.

The relationship between epistemological beliefs and teaching anxiety in mathematics

The purpose of this study is to investigate the relationship between the anxiety of teaching mathematics and epistemological beliefs of prospective teachers. Research was carried out on 279 teacher candidates studying in the primary education mathematics teaching, secondary education mathematics teaching and class teaching programs. A 23-item Mathematics Teaching Anxiety Scale and a 35-item Epistemological Belief Scale were applied to the teacher candidates included in the sampling. In the analysis of the data, the Pearson Product-Moment Correlation Coefficient analysis was applied to determine the relationship between the anxiety of teaching mathematics and epistemological beliefs. As a result of the analysis, it has been determined that a weak, negative correlation exists between the anxiety of teaching mathematics and epistemological beliefs in the teacher candidates. Key words: Mathematics, teaching anxiety, epistemological beliefs, prospective teacher.