Mathematical Problem Posing as a Measure of Curricular Effect on Students\u27 Learning

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students\u27 learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of employing a qualitative rubric to assess different characteristics of students\u27 responses to the posing tasks. Instructional and methodological implications of this study, as well as future directions for research, are discussed

The effects of providing mathematical problem -posing experiences for K--8 pre-service teachers: Investigating teachers\u27 beliefs and characteristics of posed problems

This study incorporated problem posing into a mathematics content course for preservice elementary and middle school teachers by extending George Polya\u27s (1957) problem solving heuristic to include problem re-formulation and by having participants pose problems from sets of given information. The course provided pre-service teachers with a new mathematical perspective and this research examined participants\u27 problem posing, beliefs about mathematics, and beliefs about the teaching and learning of mathematics. Study participants were enrolled in a mathematics content course for pre-service teachers at the University of New Hampshire. There were twenty students in the course and nineteen agreed to be participants in the study by allowing all of their course work to be collected. Participants consisted of 4 sophomores, 7 juniors, 6 seniors, and 2 graduate students. All participants were working towards their teaching certification and most were mathematics education majors. Four of the nineteen participants agreed to be interviewed three times each during the semester. Characteristics of participants\u27 posed problems, beliefs about mathematics, and beliefs about teaching and learning mathematics were explored using researcher developed questionnaires that were given before and after the semester. Also, all student work, journal entries, and the interviews of four participants, which were focused on topics related to beliefs about problem posing, characteristics of posed problems, beliefs about mathematics, and beliefs about teaching and learning mathematics, were collected during the instructional treatment. Problems posed by participants were organized and coded using a quantitative scale, while journal entries and interview data were analyzed qualitatively. Results showed an increase in participants\u27 problem posing efficiency and ability to pose multi-step problems. Also participants tended to utilize higher level problem re-formulation techniques as the instructional treatment progressed. Throughout the instructional treatment participants were reflecting on the role of problem posing in teaching and learning mathematics and considering both the pros and cons of including problem posing in their future classrooms and its possible effect on student learning. All participants suggested that they would incorporate student problem posing in their classrooms to help students develop ownership of mathematics and exhibit creativity

Web-based active learning and frequent feedback: Engaging first-year university students

Web-based technology is particularly well-suited to promoting active student involvement in the processes of learning. All students enrolled in a first-year educational psychology unit were required to complete ten weekly online quizzes, ten weekly student-generated questions and ten weekly student answers to those questions. Results of an online survey of participating students strongly support the viability and perceived benefits of such an instructional approach. Although students reported that the 30 assessments were useful and reasonable, the most common theme to emerge from the professional reflections of participating lecturers was that the marking of questions and answers was unmanageable

A case study of the integration of ICT in teaching and learning in a smart school in Sabah

This research investigates teachers’ views of their use of ICT in teaching and learning (T&LICT). The objective of this research was to study in depth the thoughts, beliefs and opinions of the teachers’ attempt towards pedagogical improvement as part of the Smart School Project. Specifically this research examines and describes the teachers’ implementation of T&LICT in the classroom in terms of the instructional practice, the instructional roles and the instructional environment. A case study research methodology is employed. The case is Sekolah Menengah Bestari (a psuedonym), which is a Smart School in Sabah. Analysis of data from 52 survey questionnaires complemented the qualitative data from the 13 interviews and 3 observations, as well as document analysis. Findings indicated that hardware and software technology infrastructure were available to support the T&LICT implementation. Nevertheless, the teachers felt it was not enough to implement T&LICT effectively. It was estimated that about half of Sekolah Menengah Bestari staff, mainly Bestari and ETeMS teachers, implemented T&LICT. Findings indicated that teacher practices were little changed. IT was used mainly to support the existing teacher-directed and teacher-centered approach. The role of the teacher extended to that of facilitating without releasing control of lesson to the students

Alternative Modes for Teaching Mathematical Problem Solving: An Overview

Various modes are proffered as alternatives for teaching mathematical problem solving. Each mode is described briefly, along with general purposes, advantages and disadvantages. Combinations of modes are suggested; general issues identified; recommendations offered; and feedback from teachers summarized

Criticality and Collaboration: Developing Critical Literacy Writing Instruction for Secondary Black Students

The purpose of this study was to explore the beliefs and identities of two Black ELA teachers committed to criticality and examine how these beliefs and identities affect perspectives and teaching practices. This study also explored the process through which the two teachers created instructional units of study intended to support the secondary Black student participants deepen their criticality development. Finally, the students’ writing was assessed to analyze the curriculum’s impact. This study drew upon sociocultural learning theory and critical literacy writing instruction. Critical composition pedagogy was used to design instruction with the intent to help students write for critical social change. This qualitative study also employed case study methodology and critical discourse analysis methods. Findings demonstrate how the teachers’ social justice background, cultural experiences, and pedagogical practices supported their efforts to develop critical curriculum. Through the critical discourse analytic tool, additional findings suggest the critical composition pedagogy curriculum increased student participants’ exploration of identity, investigation of community concerns, and increased their active involvement in classroom tasks. Implications highlight the importance of students writing for critical social change and the urgency of addressing challenges to critical curriculum such as administrative mandates and legislation that limit the praxis of critical literacy focused teaching and learning

Formative Assessment for Middle School Mathematics Instruction: An Evidence-based Approach to Evaluating Teacher Posing, Pausing, and Probing Moves

This study involved empirical investigation of a moves-based conceptualization of teacher practices of planning, enacting, and reflecting on formative assessment (FA) in mathematics classrooms in a high-needs school district in California. A qualitative case study of six middle school mathematics teachers’ practices of posing questions, pausing to foster equity of participation and quality of response, and probing student thinking, the study provides empirical evidence of qualitatively distinct levels of teacher posing, pausing, and probing moves. The study utilized a National Research Council-based educational assessment design framework that employed construct maps, multi-faceted items design, and scoring guides to examine teacher practice and to provide feedback protocols for teachers engaged in FA. Guided by the 2014 Standards for Educational and Psychological Testing, the study provides evidence for content validity and tools for future rater reliability investigations. The study found levels of teacher questioning practice, operationalized as posing, pausing, and proving moves, could be represented along generalized continua in the context of middle school mathematics instruction. The study’s work toward the development of a teacher learning progression framework in the formative assessment domain has implications for establishing an empirically-based, common grammar of practice in mathematics instruction and preparation