Cognition and Affect in Mathematics Problem Solving with Prospective Teachers

Currently, there is a strong political focus in Ethiopia on science, engineering, and mathematics. This to be efficient and practical strong mathematics knowledge, which is built through effective mathematics learning and problem solving, is momentous. For this in turn students’ beliefs about mathematics learning and problem solving play an important role; since students’ beliefs are vital forces in students’ mathematics learning and problem solving. Therefore, investigating students’ beliefs about mathematics learning and problem solving is essential in educational research. To address the problem quantitative approach using survey design was employed. The data was collected from four schools in West Arsi Zone using multistage sampling. The quantitative data obtained was analyzed using mean and independent samples t-test. Consequently, this study displayed that students’ beliefs about mathematics learning, and students’ beliefs about mathematics problem solving, were neutral; and there was statistically significant difference in students’ beliefs about mathematics learning and problem solving according to stream, and parents’ residence. However, even though the mean of students’ beliefs about mathematics learning and problem solving for male students was greater than that of female students, there was no statistically significant difference between male and female students in their beliefs about mathematics learning and problem solving.

Mathematics teacher education research often focuses on ways teacher education can change prospective teachers' views in ways prescribed by teacher educators. In this paper, we explore a different perspective, one that emphasises the importance of understanding the diversity of views that prospective teachers bring to their teacher education programmes, not as a basis of change, but as a platform to build upon. In doing so, we make a case for ‘aestheticising’ mathematics teacher education research and propose an arts-based approach to analysing and presenting data concerning prospective teachers views on the teaching and learning of mathematics. We exemplify this approach by presenting a fictionalised dialogue between four prospective teachers from Sweden, based on interviews conducted prior to them entering teacher education.

There is compelling evidence on the effectiveness of bibliotherapy for facilitating one’s development. Arguably, in teacher education, bibliotherapy has been shown to facilitate prospective teachers’ professional development. However, teacher educators may experience difficulties in finding relevant reading to stimulate prospective teachers’ identification process, which is essential if the application of pedagogical bibliotherapy is to be successful. This study is situated in a mathematics education course for prospective elementary school teachers and explores the features of relevant pedagogical reading via analysis of four prospective elementary school teachers’ identification processes with two case descriptions. The identification here relates to the reading of the so-called true stories; prospective teachers read stories of other prospective teachers from the same teacher education context. We outline the recommendations for the selection of reading material when applying pedagogical bibliotherapy in order to assist prospective teachers’ professional development.

It is important for students to connect with real life in mathematics courses. The aim of this study is to investigate the activities which are written by prospective primary school teachers in the context of Realistic Mathematics Education. This research is a case study of which data were collected by qualitative methods. The participants of the research included 81 prospective primary teachers who are junior students attended primary teacher department. It was asked them to write an activity suitable for primary mathematics curriculum by considering Realistic Mathematics Education principles. They were given one month to write the activities. The activities written by prospective teachers analyzed by descriptive methods in terms of learning domains, types of context and principles of Realistic Mathematics Education. Totally 36 activities were written by prospective teachers. Based on the analysis, it was observed that not all the contexts were exactly real life contexts. It was determined that prospective teacher could not distinguish routine word problems from real life problems. It can be said that theoretical knowledge of Realistic Mathematics Education is inadequate for writing activities and prospective primary teachers need to practice on writing activities regarding the mentioned theory.

This article focuses on teacher educators’ reflections on prospective teachers’ cognitive engagement in the teaching and learning of mathematics during the pandemic. Using three interacting aspects that can foster learners’ cognitive engagement as a lens, observations and reflections from two teacher educators and anonymous screenshots of students’ work were gathered and analysed by a mathematics teacher educator. The prospective teachers’ self-regulated learning, engagement in solving tasks, and participation in productive discourse were positively surprising, showing the cognitive presence of the learners during virtual teaching. The influence of digital platforms like Blackboard and digital tools like GeoGebra, Desmos, Padlet, Google Docs, Google Forms and Google Sheets in teaching helped us observe the learners’ cognitive engagement in real time.Contribution: The GeoGebra Class function and the Desmos Teacher feature helped us to observe the prospective teachers’ cognitive engagement during the online teaching. However, continuously and rapidly creating digital content on said digital platforms can be demanding for educators.

This study aimed to describe the self-regulated learning skills of prospective teachers studying at a public university in Istanbul and reveal their differences in relation to the components of these skills, namely motivation and taking action to learn, planning and goal-setting, strategy use and evaluation, and attachment in learning, as well as other variables, including their major, type of high school completed, age, gender, socioeconomic level and parents’ education level. It was also investigated whether there was a relationship between the participants’ self-regulated learning skills and their major and grade levels. The screening model was used in the research. The sample consisted of students studying at a public university in Istanbul in the 2018-2019 academic year and selected using the simple random sampling method. The participants comprised 926 first-, second-, third- and fourth-grade students attending the departments of computer education and instructional technology, classroom teaching, preschool teaching, mathematics teaching, science teaching, guidance and psychological counseling, Turkish language teaching, social studies teaching, special education, English language teaching, French language teaching, and German language teaching. The Self-Regulatory Learning Skills Scale (SRLSS) and a personal information form were used as the data collection tools. The findings of the research revealed that the prospective teachers had high scores in the subscales of SRLSS and the overall scale. It was concluded that the prospective science teachers had higher scores in planning and goal-setting than the students attending all other programs except for mathematics teaching. Furthermore, the scores of female prospective teachers in all subscales were higher than those of the male participants. Considering the type of high school, the participants that had completed basic high school scored higher in strategy use and evaluation compared to those that had finished other types of high school. When the prospective teachers’ self-regulated learning skills were analyzed according to their parents' education level, no significant difference was found. Keywords: self-regulated learning, prospective teachers, teacher education.

Effective mathematics learning plays an important role in improving the quality of education and human resources. However, many students have difficulty understanding mathematical concepts, especially in mathematical problem solving and learning independence. This study aims to analyze the influence of realistic mathematics learning models on the mathematical problem solving ability and learning independence of grade VIII students at MTs PAB 2 Sampali Medan. The research method used is quasi-experiment with a pretest-posttest control group design. The research sample consists of two classes, namely an experimental class that uses a realistic mathematics learning model and a control class that uses conventional methods. Data analysis using two-track ANAVA shows that the realistic mathematics learning model has a significant influence on improving students' mathematical problem solving ability (sig. = 0.034 < 0.05) and students' learning independence (sig. = 0.000 < 0.05). However, the results of the study also showed that there was no interaction between the learning model and students' initial mathematical ability on problem solving ability (sig. = 0.627 > 0.05) or on students' learning independence (sig. = 0.994 > 0.05). These findings indicate that the realistic mathematics learning model is effective in improving students' problem solving ability and learning independence without being affected by their initial ability level. By connecting mathematical concepts with real-life experiences, this model can help students better understand the material and become more independent in learning. Therefore, a realistic mathematics learning model is recommended as a strategy in improving the quality of mathematics learning in schools.

The sensory characteristics of teachers and prospective teachers directly affect them and their teaching activities. It is important to examine in detail how the attitude and anxiety levels of prospective primary teachers towards the teaching profession change throughout the years they receive education. This study aimed to cross-sectionally and longitudinally examine whether the attitude and anxiety levels of prospective primary school teachers towards the teaching profession changed throughout their undergraduate education and determine the factors/experiences triggering this change in accordance with the qualitative data obtained. A cross-sectional study was carried out with the participation of 1085 prospective teachers. For the longitudinal study, quantitative and qualitative data were collected together from 57 prospective teachers over a period of four years. Attitude scale regarding teaching and occupational anxiety scale for prospective teachers were used for data collection. The results of both the cross-sectional and longitudinal studies showed that the attitude scores of the participants did not change in accordance with the grade level. However, it was determined that the anxiety scores of the participants decreased as the grade level increased. The results revealed that this change is statistically significant. The qualitative results revealed that internship practices and direct experiences had a great influence on this change.

Having cognitive competence in mastering learning theory and designing learning is one of the important competencies for prospective teachers to have. The description of prospective teacher competence is important for lectures to follow up. One approach to learning in mathematics is Realistic Mathematic Education (RME). RME is a student-centered approach to learning mathematics adopted from the Netherlands and holds to the principle that mathematics is a human activity. This learning approach has been implemented massively in the last few decades in Indonesia and has had a positive impact so this approach is important to teach. However, there are still many prospective elementary teachers who do not know and understand what and how to implement RME itself. Because of the importance of the cognitive competence that prospective elementary teachers must have regarding this RME approach, further research is needed on this matter. The aim of this study is to describe how the cognitive abilities of prospective elementary teachers on RME approach with the application of cooperative learning. The method used in this study was descriptive qualitative with observation and survey data collection techniques which were analyzed using cognitive levels according to PISA and Anderson on 50 prospective elementary teachers in Yogyakarta State University or in Bahasa Universitas Negeri Yogyakarta (UNY) 4th semester students. The results of this study were that most students had a fairly good theoretical understanding of RME. Although to apply it in learning mathematics requires more training, especially in designing contextual problems and how to evaluate them with various other approaches in learning mathematics.

Mathematical Modelling and Technology in Teacher Education – Visions and Reality

A framework for prospective primary teachers’ knowledge of mathematical reasoning processes

This innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education, psychology of education, technology education, mathematics popularization, and more. The volume’s three major themes - technology, creativity, and affect - represent key issues that are crucially embedded in the activity of problem solving in mathematics teaching and learning, both within the school setting and beyond the school. Through the book’s new pedagogical perspectives on these themes, it advances the field of research towards a more comprehensive approach on mathematical problem solving. Broadening the Scope of Research on Mathematical Problem Solving aims to provide a valuable resource for researchers and teachers interested in mathematical problem solving, as well as researchers and teachers interested in technology, creativity, and affect.

Features of two lesson study contexts, one with prospective secondary teachers engaged in microteaching lesson study and one with prospective elementary teachers engaged in field experiences, were investigated for providing US prospective teachers with opportunities for growth as teachers of mathematics. In both contexts, the prospective teachers (PTs) exposed their knowledge, beliefs and practices to the scrutiny of peers and other experts, developing and reconsidering their thinking and practices through the shared teaching experiences. Similarities and differences in features of the two contexts are discussed with respect to PT learning. Similarities included the importance of negotiation during teaching cycles as catalysts for PT learning, the value of the cooperative nature of the experiences for sharing varying ideas and perspectives among PTs, the merits of overarching student learning goals for PT lesson planning, and the contributions of the group products (written or oral reports of the lesson study) to the learnercenteredness of the experiences. Differences influencing prospective teacher learning included the extent of focus on mathematics knowledge, extent of focus on classroom processes and management, use of videotaped lessons as part of formative feedback, and participation of knowledgeable advisors during or at the end of the cycles.

This research aims to analyze the effect size of using the Project-Based Learning (PjBL) model on problem-solving abilities in mathematics learning and investigate the effect size based on educational levels. The research method employed is quantitative with meta-analysis, aiming to summarize, evaluate, and integrate the results of several published studies. Data collection techniques involve documentary studies by searching national and international journals published between 2015 and 2023. A total of 24 studies met the predetermined inclusion and exclusion criteria, and the effect sizes of each study were calculated. Subsequently, the overall average effect size and effect sizes based on educational levels were calculated. Data analysis was conducted using JASP software version 0.18.1.0. The results of this research indicate that the effect size of the Project-Based Learning model on problem-solving abilities in mathematics learning is significantly large, with an effect size of 0.973. Furthermore, statistically significant differences were reported in the effect sizes of the PjBL model on problem-solving abilities in mathematics learning across educational levels. The implementation of the PjBL model has a very large effect size on problem-solving abilities in mathematics learning for elementary, and college-level students. Meanwhile, at junior high school and the senior high school level, the PjBL model on problem-solving abilities in mathematics learning has a large and amoderate effect size.

Bu araştırmanın amacı matematik öğretmen adaylarının matematiksel muhakeme etme kavramına yönelik öz yeterlik inançlarını konu edinen bir değerlendirme yapmaktır. Bu amaç doğrultusunda öğretmen adaylarının matematiksel muhakeme etme öz yeterlik düzeyleri ve bir problemde yer alan matematiksel muhakeme etme göstergelerini belirleyebilme durumları arasında bir değerlendirme yapılmıştır. Araştırmada nicel araştırma yöntemlerinden biri olan tarama deseni kullanılmıştır. Araştırmanın çalışma grubunu 51 matematik öğretmen adayı oluşturmaktadır. Araştırmada kullanılan veri toplama araçları “Matematiksel Muhakeme Öz-Yeterlik Ölçeği”, “Matematiksel Muhakeme Etme Problemleri” ve “Matematiksel Muhakeme Etme Göstergeleri Tablosu” dur. Araştırmanın sonucunda, öğretmen adaylarının matematiksel muhakemeye yönelik öz yeterliklerinin ölçek ortalamasının üstünde olduğu ve öz yeterliklerinin yaratıcı düşünme alt boyutunda en düşük, ilişkilendirme alt boyutunda ise en yüksek olduğu belirlenmiştir. Öğretmen adayları matematik problemlerinde yer alan matematiksel muhakeme etme göstergelerini belirleyebilme açısından yeterince başarılı olamamışlardır. Bunlara ek olarak öğretmen adaylarının matematiksel muhakeme etme öz yeterlik düzeylerinin matematiksel muhakeme etme problemlerinde yer alan matematiksel muhakeme etme göstergelerini belirleyebilme durumları üzerinde istatistiksel olarak anlamlı bir etkisinin olduğu görülmüştür. Sonuç olarak öğretmen adaylarının matematiksel muhakeme etmelerinin desteklenmesi ve matematiksel muhakeme etmeye yönelik içsel inançlarının güçlendirilmesi onların ilgili alanda donanımlı birer öğretmen olmalarına katkı sağlayacaktır.