The Zoo Connection: A Cooperative Project Between Formal and Informal Educational Institutions

This project was a cooperative effort between university faculty, elementary school teachers, and members of the Education Department at the Indianapolis Zoo. The purpose of this project was to develop, evaluate, and disseminate a set of fourteen K-6 science lessons that could be used in conjunction with field trips to the zoo. These lessons, titled The Zoo Connection, follow the Learning Cycle teaching model. In addition to following the model, the development of the lessons was based on the premise that teachers should focus on a specific science concept or set of related concepts when visiting a zoo. Workshop sessions were conducted to introduce teachers to the materials and to provide them with strategies for implementing the materials in their science instruction. An evaluation was conducted for each workshop session to determine teachers' perceptions of the materials and to determine whether they felt prepared to use them with their students. The materials were also field-tested in several elementary schools to assess their effectiveness for presenting science concepts to elementary school children. Results indicate that teachers felt the workshops adequately prepared them to use the materials and that the materials were effective for presenting science concepts.     

Preservice Teacher Beliefs About Proofs

This article describes a study of backgrounds, beliefs, and attitudes of teachers about proofs. Thirty preservice elementary teachers enrolled in a mathematics content course and 21 secondary mathematics teachers in an abstract algebra course were surveyed. The study explored four issues: preservice teachers' experiences/exposure to proof, their beliefs about what constitutes a proof and the role of proof in mathematics, and their beliefs about when proof should be introduced in grades K-12. Results of the survey are described as a means for discussing the backgrounds and beliefs future teachers hold with regard to teaching proofs in their own classrooms. Finally, a short collection of sample explorations and questions, which could be used to encourage the thinking and writing of proofs in grades K-12, is provided. One of these questions was posed to 215 secondary students; examples of their reasoning and a discussion of the various techniques employed by the students are included.     

An International Project for the Development of Data Handling Skills of Teachers and Pupils

In this paper we provide an overview of the international CensusAtSchool project, designed, written and implemented first in the UK from October 2000 - April 2001 for pupils aged 7 -16 in primary and secondary schools. It has been adapted for similar aged school children in South Africa and Australia and was implemented in those countries in July and October 2001, respectively. We present our motivation, aims and objectives for carrying out such a project and show some results of analysis from the returns we have received from all three countries. Key outputs from the project include: worksheets that are suitable for enhancing data handling skills of pupils; a training course that wraps information and communications technology with data handling skills that is suitable to enhance the professional development of teachers; a raised awareness amongst pupils and teachers of the need to properly collect, present and analyze primary data; a contribution to improving the statistical numeracy and thinking skills of both teachers and pupils.     

Eliciting and Developing Teachers' Conceptions of Random Processes in a Probability and Statistics Course

The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses within a collaborative course design were used to support a teaching experiment about teachers' conceptions of random processes. In particular, teachers were asked whether the outcomes of Rock-Paper-Scissors (RPS) are generated randomly or not, were presented with a definition for random selection, and were asked to come to a conclusion about RPS. Teachers struggled to reconcile the equality of winning outcomes for each player with the potential for human interference in the process of generating outcomes. Ultimately, teachers concluded the outcomes were not generated randomly, but encountered a variety of unexpected obstacles along the way.     

Elementary preservice teachers' integration of engineering into STEM lesson plans

Science, technology, engineering, and mathematics (STEM) integration is a desired outcome according to Next Generation Science Standards. However, learning to teach integrated STEM content has been challenging for teachers. Consequently, the purpose of this qualitative study was to describe how 16 preservice teachers enrolled in a mathematics methods course created integrated STEM lesson plans that incorporated an authentic engineering problem. Content analysis of the completed integrated STEM lesson plans used the Quality K-12 Engineering Education Framework to identify any characteristics of engineering. We found that 15 of 16 preservice teachers demonstrated at least an emerging ability to create an integrated STEM lesson that contained an engineering problem, constraints, a prototype or model, model testing, and data collection and analysis related to the model. We concluded that giving preservice teachers opportunities to experience engineering design problems could better prepare them to design and implement integrated STEM education in their classrooms. The findings from this study have practical implications for mathematics methods teacher educators who teach the pedagogy behind STEM education. This study also has theoretical implications because socially situated learning theory was extended to Model-Eliciting Activities and connected them to the K-12 Framework for Quality Engineering Education.     

An inquiry-oriented approach to undergraduate mathematics

To improve undergraduate mathematics learning, teachers need to recognize and value characteristics of classroom learning environments that contribute to powerful student learning. The broad goal of this special issue is to share such characteristics and the theoretical and empirical grounding for an innovative approach in differential equations called the Inquiry Oriented Differential Equations (IO-DE) project. We use the IO-DE project as a case example of how undergraduate mathematics can build on theoretical and instructional advances initiated at the K-12 level to create and sustain learning environments for powerful student learning at the undergraduate level. In addition to providing an overview of the five articles in this special issue, we highlight the theoretical background for the IO-DE project and provide a summary of two quantitative studies done to assess the effectiveness of the IO-DE project on student learning.     

Teaching mathematical modelling through project work

The paper presents and analyses experiences from developing and running an inservice course in project work and mathematical modelling for mathematics teachers in the Danish gymnasium, e.g. upper secondary level, grade 10~12. The course objective is to support the teachers to develop, try out in their own classes, evaluate and report a project based problem oriented course in mathematical modelling. The in-service course runs over one semester and includes three seminars of 3, 1 and 2 days. Experiences show that the course objectives in general are fulfilled and that the course projects are reported in manners suitable for internet publication for colleagues. The reports and the related discussions reveal interesting dilemmas concerning the teaching of mathematical modelling and how to cope with these through «setting the scene» for the students modelling projects and through dialogues supporting and challenging the students during their work. This is illustrated and analysed on the basis of two course projects.     

Crossing the Barriers Between Preservice and Inservice Mathematics Teacher Education: An Evaluation of the Grant School Professional Development Program

A 2‐year school‐based mathematics professional development program is described and evaluated after its first year of implementation. Included in this program as its first course was a unique methods course in elementary education involving both preservice students and inservice teachers who cooperatively studied and applied reform pedagogy. The program resulted from the collaborative efforts of two institutions of higher education, a neighboring school district, the principal and teachers of one school within that district, and the state office of education. Evaluation of the first year of the program consisted of assessing the beliefs and perceptions of both preservice students and inservice teachers, along with an assessment of the mathematical achievement of the children within the classes of those teachers. Pre‐ and post‐assessments of the preservice students and inservice teachers' beliefs regarding reform pedagogy were administered using the IMAP [Integrating Mathematics and Pedagogy] Web‐Based Beliefs Survey (2006). Likert scale surveys were used to assess perceptions regarding course climate and participant relationships from both teacher groups. The mathematical achievement of children was assessed in three ways: The Wide Range Achievement Test‐3 ( Stone, Jastak, & Wilkinson, 1995 ), the Utah state criterion‐referenced assessment, and performance assessments developed specifically for use at the school. Data obtained from all sources indicated positive effects upon teachers and children, thus providing substantial evidence in support of both the value of the methods course itself and the overall professional development program. An additional evaluation will be conducted following the second year of the program.     

Effectiveness of a Mathematics Methods Course in Reducing Math Anxiety of Preservice Elementary Teachers

In an attempt to find ways of reducing the mathematical anxiety of preservice elementary teachers, three cases were investigated. The first was a section of mathematics for elementary teachers taught in a very traditional manner, and the second was the same course taught in a manner consistent with the recent recommendations of the National Council of Teachers of Mathematics. The third case included two sections of a methods course which covered the same mathematical content, as well as addressing how it should be taught to children. The Mathematics Anxiety Rating Scale for Adults was administered before and after the courses. No significant reduction of anxiety was measured in either mathematics section, but both sections of the methods course showed a significant reduction.     

Adapting Japanese Lesson Study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: a case study

Increased efforts are needed to meet the demand for high quality mathematics in early years classrooms. Despite the foundational role of geometry and spatial reasoning for later mathematics success, the strand receives inadequate instructional time and is limited to concepts of static geometry. Moreover, early years teachers typically lack both content knowledge and confidence in teaching geometry and spatial reasoning. We describe our attempt to deal with these issues through a research initiative known as the Math for Young Children project. The project integrates effective features of both design research and Japanese Lesson Study and is designed to support teachers in developing content knowledge and new approaches for teaching geometry and spatial reasoning. Central to our Professional Development model is the integration of four adaptations to the Japanese Lesson Study model: (1) teachers engaging in the mathematics, (2) teachers designing and conducting task-based clinical interviews, (3) teachers and researchers co-designing and carrying out exploratory lessons and activities, and (4) the creation of resources for other educators. We present our methods and the results of our adaptations through a case study of one Professional Learning Team. Our results suggest that the adaptations were effective in: (1) supporting teachers’ content knowledge of and comfort level with geometry and spatial reasoning, (2) increasing teachers’ perceptions of young children’s mathematical competencies, (3) increasing teachers’ awareness and commitment for the inclusion of high quality geometry and spatial reasoning as a critical component of early years mathematics, and (4) the creation of innovative resources for other educators. We conclude with theoretical considerations and implications of our results.     

Prospective elementary teachers’ claiming in responses to false generalizations

When faced with a false generalization and a counterexample, what types of claims do prospective K-8 teachers make, and what factors influence the type and prudence of their claims relative to the data, observations, and arguments reported? This article addresses that question. Responses to refutation tasks and cognitive interviews were used to explore claiming. It was found that prospective K-8 teachers’ claiming can be influenced by knowledge of argumentation; knowledge and use of the mathematical practice of exception barring; perceptions of the task; use of natural language; knowledge of, use of, and skill with the mathematics register; and abilities to technically handle data or conceptual insights. A distinction between technical handlings for developing claims and technical handlings for supporting claims was made. It was found that prudent claims can arise from arguer-developed representations that afford conceptual insights, even when searching for support for a different claim.     

Putting the Fun Into Functions Through the Use of Manipulatives,Computers, and Calculators

For six years, the authors have conducted a series of professional development workshops for teachers in Grades K-8. This article summarizes some of the research from those workshops and gives an overview of the approach taken. The institutes emphasized basic reasoning skills based upon the NCTM Standards and the Kentucky Education Reform Act, integrating manipulative materials and technology. The article demonstrates the integration of manipulatives and technology using patterns, relations and functions as examples.     

How some research mathematicians and statisticians use proof in undergraduate mathematics

The paper examines the roles and purposes of proof mentioned by university research faculty when reflecting on their own teaching and teaching at their institutions. Interview responses from 14 research mathematicians and statisticians who also teach are reported. The results suggest there is a great deal of variation in the role and purpose of proof in and among mathematics courses and that factors such as the course title, audience, and instructor influence this variation. The results also suggest that, for this diverse group, learning how to prove theorems is the most prominent role of proof in upper division undergraduate mathematics courses and that this training is considered preparation for graduate mathematics studies. Absent were responses discussing proof's role in preparing K-12 mathematics teachers. Implications for a proof and proving landscape for school mathematics are discussed.     

Family Mathematics Nights: An Opportunity to Improve Preservice Teachers' Understanding of Parents' Roles and Expectations

Providing preservice teachers with opportunities to engage with parents and begin to see them as collaborators in their children's education is a persistent challenge in mathematics methods courses and teacher preparation programs more broadly. We describe the use of family mathematics nights as a model for engaging parents and preservice teachers. These events helped preservice teachers feel more comfortable in working with parents, while also giving them a friendly space for learning more about parents, the ways they work with their children, and activities they do with their children. Incorporating surveys about parents' needs and suggestions for preservice teachers allowed us to use the results as a catalyst for fostering discussions around parent engagement later in the methods course.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.     

Enhancing the pedagogy of mathematics teachers (EPMT) project: a hybrid model of professional development

Enhancing the pedagogy of mathematics teachers (EPMT) project is a hybrid model of professional development (PD) that reflects a gradual shift in the centre of gravity away from the University-based, “supply-side”, “off-line” forms of knowledge production conducted by university scholars for teachers towards an emergent school-based, demand-side, on-line, in situ forms of knowledge production conducted by teachers with support from university scholars. The aims of the EPMT project were threefold: to provide teachers with training, to facilitate teachers’ work (practice and feedback) at the school level and to enthuse and support teachers to contribute towards the development of fellow teachers. This paper examines two project participants’ infusion of their learning in classroom practice. From the lessons enacted by the two teachers it was apparent that both teachers were able to apply their learning in their lessons. The teachers also manifested changes in their perception of teaching mathematics.     

Using video to teach future teachers to learn from teaching

Video is commonly used in teacher preparation programs. Teacher educators use video for various purposes. In this study, we describe the Learning to Learn from Mathematics Teaching project. In this project, video is used to develop pre-service teachers’ (PSTs) orientations, knowledge and skills for analyzing and reflecting on mathematics teaching in ways that generate knowledge for improvement. We discuss the ways we have used video in a course aimed at developing elementary PSTs’ abilities to learn from teaching. In addition, we report on a study that investigated PSTs’ changes in lesson analysis abilities as a result of participating in the course.