Mathematics Instruction

As we have noticed from our own classroom experiences, children often find it difficult to identify the adequate operations learned in mathematics class when they are solving mechanical-operators problems in Technology class. We wanted to design a project that exploits the idea of a hands-on relationship between mathematics and technology to teach students the concept of "transmission coefficient" in schools. Our purpose was to bridge mathematical knowledge and mechanical parts in technological devices. Our belief was that visual-tangible representations enhance human cognition by scaffolding the information process. We supplied a kit with rubber foam ("Fomi") and balsa wood parts to construct an analogical clock. This included a series of gears to work with three different ratios. The project was conducted in 2007 and 2008, with 38 students ranging from 10 to 14 years of age. The students were from the 5th and 7th grades in two different schools. The project inc...

This study is aimed to design activities that improve creative thinking skills and to observe the effects of this teaching method supported by these improved activities on students’ academic successes and their creativity in an web-based learning environment, which is an another type of distance education. Within this direction, an authentic course content is formed targeting to improve the students’ high level thinking skills by differentiating the objectives of ‘The Numerals’ learning domain in Math courses of 6th grade primary school level.
Pretest-posttest control group experimental design which is a type of experimental model was used in the study. The study is held with a number of 124, 6th grade students having their education in Orhangazi Primary School between 2012-2013 school year. In the context of the research, four classes are chosen with the method of randomly assigning. Traditional teaching methods and techniques are applied to the two of the classes while the other two are treated with the web based teaching method. In addition to that, in each one of the classes which is treated with both the web based and traditional teaching methods, the activities, designed by the researcher to improve the students’ creative thinking skills, are applied. The activities used in the study are prepared in accordance with the interviews made with the experts in the field of creativity.
The data of the research are gathered via Torrance Creative Thinking Test Verbal Forms of A and B, and the academic success tests and interview forms, designed by the researcher. The convenience of the quantitative data of the study to the normal distribution is defined with the statistics of Shapiro Wilk W test. In order to analyze the normal distribution data, Dependent and Independent Samples T-Test of the Parametric Tests are used and for the data, not showing a normal distribution, non-parametric tests of Mann Whitney U and Wilcoxon Signed Rank test are used. The qualitative data of the study is analyzed with Nvivo 10 program and presented in the graphics according to the frequency of repetition and percentiles.
According to the findings of the study, web based learning improves the academic achievements and creativities when compared to the traditional teaching methods. And it is also observed that the creativity improving activities, used in the classrooms educated with the traditional methods, affect the academic achievement and creativity positively, too. Together with these, it is defined that the academic achievement and the creativity is best enhanced with the web based learning environment supported with the creative activities. The results of the study show us that web based learning is an effective way of improving high level thinking skills and this effect is considered to be strengthened through the creativity improving  activities.

As we have noticed from our own classroom experiences, children often find it difficult to identify the adequate operations learned in mathematics class when they are solving mechanical-operators problems in Technology class. We wanted to design a project that exploits the idea of a hands-on relationship between mathematics and technology to teach students the concept of ‘transmission coefficient’ in schools. Our purpose was to bridge mathematical knowledge and mechanical parts in technological devices. Our belief was that visual-tangible representations enhance human cognition by scaffolding the information process. We supplied a kit with rubber foam (Fomi) and balsa wood parts to construct an analogical clock. This included a series of gears to work with three different ratios. The project was conducted in 2007 and 2008, with 38 students ranging from 10 to 14 years of age. The students were from the 5th and 7th grades in two different schools. The project included six stages of both theory and hands-on work. In a final stage, the students were given a written test. All students were able to make workable systems of their design for a time-measuring device. This proved important for technological education. On the other hand, manipulating gears along with visual reasoning strategies allowed all students to achieve an understanding of operations with fractions. We think this is a major achievement in mathematical education.

As we have noticed from our own classroom experiences, children often find it difficult to identify the adequate operations learned in mathematics class when they are solving mechanical-operators problems in Technology class. We wanted to design a project that exploits the idea of a hands-on relationship between mathematics and technology to teach students the concept of "transmission coefficient" in schools. Our purpose was to bridge mathematical knowledge and mechanical parts in technological devices. Our belief was that visual-tangible representations enhance human cognition by scaffolding the information process. We supplied a kit with rubber foam ("Fomi") and balsa wood parts to construct an analogical clock. This included a series of gears to work with three different ratios. The project was conducted in 2007 and 2008, with 38 students ranging from 10 to 14 years of age. The students were from the 5th and 7th grades in two different schools. The project included six stages of both theory and hands-on work. In a final stage, the students were given a written test. All students were able to make workable systems of their design for a time-measuring device. This proved important for technological education. On the other hand, manipulating gears along with visual reasoning strategies allowed all students to achieve an understanding of operations with fractions. We think this is a major achievement in mathematical education.

In this paper, high school mathematics teachers’ views on computer-assisted mathematics instruction and on computer algebra systems (CAS) were explored in two stages, before and after they were trained on it. This study is based on the case study model of the qualitative research method. Semi-structured interview forms constitute the data of the study. Some codes and themes were established with the descriptive and content analyses of the data. The results show that teachers had positive opinions about computer-assisted mathematics instruction before they were trained, yet a majority of them was not able to use it in their classes for several reasons. However, it is seen that none of the teachers except for one knew about computer algebra systems (CAS). It is understood after the training that all the teachers wanted to use computer-assisted mathematics instruction in their classes, and thus they needed to use Mathematica, which is a computer algebra system, during the process. Likewise, while most of the teachers did not want their students to interact with computers or tablets in their classes before the computer-assisted mathematics instruction training, almost all of them had a favorable opinion of it after the training.

The purpose of this research was to study the procedure of think pair share, the type of cooperative learning models, which can be implemented in mathematics instruction in Manokwari, West Papua Indonesia. This study was conducted at Senior High School in Manokwari (SMA Negeri 1), Manokwari West Papua Indonesia. The research was carried out using research and development methods. The Think Pair Share learning model was modified to get the procedure of implementation in accordance with the characteristics of students studying mathematics in Manokwari, West Papua. The results of the research showed that there were two principals in the application of the think pair share model in mathematics instruction in Manokwari West Papua, selection of group members and the determination of the number of group members. Students individually start thinking of finding answers to the assignment submitted. Group members must consist of students who already know each other well, but should not to have a similar level of knowledge, while the number of group members must start from two students.

This study examined interventions for addition and subtraction that were implemented through single-case design (SCD) research studies. We attempted to extend prior SCD meta-analyses by examining differences in effect sizes across several moderating variables and by including a novel index of effect, improvement rate difference (IRD). We also examined the extent to which effect sizes differed by degree of experimental control achieved in the studies. Forty-seven effect sizes were obtained across 11 studies. IRD effect sizes ranged from .59 to .90 and suggested a moderate to large effect for the math interventions. Variables that appeared to moderate the effects were student age, time spent in intervention, and intervention type. We also identified a relationship between experimental control and the obtained effect sizes. Findings indicated that further SCD research in basic arithmetic and rigorous experiments are necessary to establish an evidence base that accurately characterizes intervention effectiveness.

This paper reports on a case study that was conducted at five high schools from a large, urban school district located in South Texas. The purpose of the study was to gain an understanding of Algebra 1 teaching strategies. The research questions were: (1) What is the predominant mode of instruction for Algebra 1? and (2) What is the level of achievement of Algebra 1 students? The schools consist primarily of students of Mexican descent. The teachers were also of Mexican descent. Both qualitative and quantitative data were collected. Field observations revealed a teaching methodology that focused on skills and procedures facilitated through lecture and supervised practice. The instruction was heavily influence by the state's high stakes test. Student achievement reflected the instructional methodology, which focused on particular skills and processes. Students failed to complete open-ended and higher order thinking questions on a standardized measure of algebraic skills and conc...

Οι αντωνυμίες στο διάλογο κωδικοποιούν τη διαδραστική λειτουργία της γλώσσας και βοηθούν τον εκπαιδευτικό με το κύρος του και την διδακτική του επιρροή να καθοδηγήσει τους μαθητές σε μαθηματικές γενικεύσεις, μέσα από τη διδακτική διαδικασία (Rowland, 1999). Οι μαθητές με τη βοήθεια του διαλόγου μπορούν να αναπτύξουν λεξιλόγιο και να το χρησιμοποιήσουν με πολλαπλούς τρόπους, για παράδειγμα για να καταφέρουν να εισέλθουν σε ευρύτερες γνωστικές κοινότητες (Mercer, 2000).

Learning through social media platforms is a nascent pedagogy that opens up new virtual online e-instructional modalities and avenues to be explored especially in these challenging emergency times of COVID-19. This research focuses on a self-directed initiative of a math teacher who taught her students in an open virtual class via Instagram. This study explores how the main features of Instagram -inherently used as social interaction platform - were maximized for educational purposes. It also investigates the effects, be they positive or negative, on the learning-teaching process in terms of engagement and communication. For this, a mixed-method sequential exploratory design was opted for to conduct the study which surveyed 100 students across 22 different high schools who took part in the virtual open math classes. The findings highlight the different patterns of Instagram use and platform features that lend this social media website the requisite feasibility to educationalize it. ...

The purpose of this study was to examine the relations between teachers’ reports on self-regulatory strategy use in mathematics instruction and individual motivational and affective factors. Two hundred and ninety two Greek primary school teachers responded to two questionnaires assessing: a. the strategies they use themselves to plan, monitor, and evaluate mathematics instruction, and b. the strategies they use to activate and enhance students’ self-regulated learning in mathematics. Path analysis showed that teachers’ self-regulation strategies both for their own teaching and for enhancing students’ self-regulation in mathematics were predicted by their self-efficacy beliefs in teaching mathematics, the value they attribute to mathematics, and their emotional commitment to their profession. Teachers’ enjoyment of mathematics teaching did not directly predict their reported use of self-regulatory instructional strategies. The implications of the study are related to the development of teachers’ training programs in self-regulated instruction.

Teacher quality has become a national policy concern in the US, especially in mathematics. This study provides insights into the conceptualisation of high quality mathematics teaching from the perspective of approximately 750 students in grades nine through twelve. Results from Rasch analysis yield information about the quality of theMathematics Quality Survey constructed for this study and the hierarchy of items representing varying levels of quality as perceived by the students. Group interviews with teachers and open-ended responses from students are used to support the findings. This study lays the groundwork for understanding the difference between being qualified and being a quality teacher.