Training Master's‐Level Graduate Students to Use Inquiry Instruction to Teach Middle‐Level and High‐School Science Concepts

Through the GK‐12 program of the National Science Foundation, graduate student fellows in a coastal marine and wetland studies program were trained to present targeted science concepts to middle‐ and high‐school classes through their own research‐based lessons. Initially, they were taught to follow the 5‐E learning cycle in lesson plan development, but a streamlined approach targeting the three attributes of science concepts—macroscopic, model, and symbolic—was found to be a better approach, while still incorporating key facets of the 5‐E model. Evaluation of the level of inquiry in the classrooms was determined using an inquiry scale from 0 to 4, differentiated by the relative number of actions that are student‐centered. The graduate fellows consistently delivered lessons at the targeted levels 2 or 3, guided inquiry. In order to assess student learning, the GK‐12 fellows were trained to develop single‐item pre‐ and post‐assessments designed to probe middle‐level and high‐school students' understanding of the macroscopic, model, and symbolic attributes of targeted science concepts. For the lessons based on the research of the fellows, about 80% of the students showed statistically and practically significant learning gains. The GK‐12 fellows positively impact the classroom and are effective science ambassadors.     

Preparing K‐8 Preservice Teachers in a Content Course for Standards‐Based Mathematics Pedagogy

Many K–8 preservice teachers have not experienced learning mathematics in a standards‐based classroom. This article describes a mathematics content course designed to provide preservice teachers experiences in learning mathematics that will help build a solid foundation for a standards‐based methods course. The content course focuses on developing preservice teachers' mathematical knowledge, as well as helping them realize what it means to learn mathematics that is taught using the pedagogy in the Principles and Standards for School Mathematics ( National Council of Teachers of Mathematics, 2000 ). Furthermore, findings are presented from a study on this course that describe students' pre‐ and postcourse beliefs, attitudes, and perceptions of what it means to learn and teach mathematics. These findings provide evidence that the students in the study are beginning to understand what is meant by a standards‐based classroom. Data were collected from surveys and interviews. Quotes from the students who aspire to be elementary teachers are used throughout the article to support the points.     

Applying Mathematical Concepts with Hands‐On,Food‐Based Science Curriculum

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the Food, Math, and Science Teaching Enhancement Resource (FoodMASTER) Intermediate curriculum on fourth‐grade students' mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20‐item researcher‐developed mathematics knowledge exam (intervention n = 288; control n = 194). Overall, the results showed a significant increase in mathematics knowledge from pretest to posttest. These findings suggest that the food‐based science activities provided the students with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students' mathematics knowledge while building a foundation for becoming quantitatively literate adults.     

Community‐Based Service‐Learning as a Source of Personal Self‐Efficacy: Preparing Preservice Elementary Teachers to Teach Science for Diversity

Bandura (1997) contends that when compared to other sources of efficacy, mastery experiences, when presented appropriately, have the most powerful influence on self‐efficacy. The purpose of this study was to investigate the effects of community‐based service learning (CBSL) experiences on preservice elementary teachers' personal self‐efficacy beliefs about equitable science teaching and learning. Data were collected using pretests‐posttests and post‐questionnaires with the study sample. Findings from this study support Bandura's assertion. CBSL experiences were an important source of personal self‐efficacy and significantly influenced preservice elementary teachers' personal self‐efficacy beliefs about equitable science teaching and learning.     

Prospective Teachers' Perspectives on Mathematics Teaching and Learning: Lens for Interpreting Experiences in a Standards‐Based Mathematics Course

In a mathematics course for prospective elementary teachers, we strove to model standards‐based pedagogy. However, an end‐of‐class reflection revealed the prospective teachers were considering incorporating standards‐based strategies in their future classrooms in ways different from our intent. Thus, we drew upon the framework presented by Simon, Tzur, Heinz, Kinzel, and Smith to examine the prospective teachers' perspectives on mathematics teaching and learning and to address two research questions. What perspectives on the learning and teaching of mathematics do prospective elementary teachers hold? How do their perspectives impact their perception of standards‐based instruction in a mathematics course and their future teaching plans? Qualitative analyses of reflections from 106 prospective teachers revealed that they viewed mathematics as a logical domain representative of an objective reality. Their instructional preferences included providing firsthand opportunities for elementary students to perceive mathematics. They did not take into account the impact of a student's conceptions upon what is learned. Thus, the prospective teachers plan to incorporate standards‐based strategies to provide active experiences for their future elementary students, but they fail to base such strategies upon students' current mathematical conceptions. Throughout, the need to address prospective teachers' underlying perspectives of mathematics teaching and learning is stressed.     

Using Sociocultural Theory to Teach Mathematics: A Vygotskian Perspective

This study describes an elementary teacher's implementation of sociocultural theory in practice. Communication is central to teaching with a sociocultural approach and to the understanding of students; teachers who use this theory involve students in explaining and justifying their thinking. In this study ethnographic research methods were used to collect data for 4 1/2 months in order to understand the mathematical culture of this fourth‐grade class and to portray how the teacher used a sociocultural approach to teach mathematics. To portray this teaching approach, teaching episodes from the teacher's mathematics lessons are described, and these episodes are analyzed to demonstrate how students created taken‐as‐shared meanings of mathematics. Excerpts from interviews with the teacher are also used to describe this teacher's thinking about her teaching.     

Preparing Pre‐Service Teachers to Teach Mathematics in Inclusive Classrooms: A Three‐Year Case Study

Federal and state regulations mandating inclusion of students with disabilities in general education classes have made it essential to create pathways for pre‐service teachers to develop skills to teach content to diverse groups of students. The study uses a framework suggested by the relationship between teacher attitude and teacher behavior ( Fullan, 1982 ), teacher beliefs and practice, and self‐efficacy and behavioral change ( Bandura, 1977 ). The purpose of the study was to examine changes, if any, in three cohorts of general education teacher candidates' (n=13, n=8, n=5) attitudes toward teaching mathematics to students with disabilities after participating in focused instructional experiences which provided both information and vicarious positive teaching activities in special education. Data collected included pretest and posttest scores for each of the three cohorts and journal entries. Little or no change in attitude towards students with disabilities and mathematics, and efficacy to teach students with disabilities was observed for the year one and year two cohorts. In the third year the modules were combined with a structured field experience. The data collected from the third year cohort suggested a positive trend in attitude as measured by the survey data and field experience journal data. Future study with larger samples is needed.     

Secondary Options and Post‐secondary Expectations: Standards‐based Mathematics Programs and Student Achievement on College Mathematics Placement Exams

Research on student achievement within the University of Chicago School Mathematics Project (UCSMP) and Core‐Plus Mathematics Project (CPMP) at the secondary level is beginning to accumulate, however, much less is known about how prepared these students are for post‐secondary education. Therefore this study involving students within one tracked school district used multiple linear regression to examine the role of differential experience within two secondary Standards‐based mathematics programs, gender, and prior mathematics achievement on college algebra and calculus readiness placement test scores. Results show that there are no significant differences between students who had completed three and four years of the CPMP curriculum. UCSMP students with four or five years of experience significantly outperformed CPMP students on both assessments. Prior achievement was a significant predictor of student achievement on both examinations. Male students outperformed female students on the algebra placement exam. Students who had studied from both CPMP and UCSMP significantly outperformed students who had studied from CPMP for four years on the calculus readiness examination.     

Using self‐dissimilarity to quantify complexity

For many systems characterized as “complex” the patterns exhibited on different scales differ markedly from one another. For example, the biomass distribution in a human body “looks very different” depending on the scale at which one examines it. Conversely, the patterns at different scales in “simple” systems (e.g., gases, mountains, crystals) vary little from one scale to another. Accordingly, the degrees of self‐dissimilarity between the patterns of a system at various scales constitute a complexity “signature” of that system. Here we present a novel quantification of self‐dissimilarity. This signature can, if desired, incorporate a novel information‐theoretic measure of the distance between probability distributions that we derive here. Whatever distance measure is chosen, our quantification of self‐dissimilarity can be measured for many kinds of real‐world data. This allows comparisons of the complexity signatures of wholly different kinds of systems (e.g., systems involving information density in a digital computer vs. species densities in a rain forest vs. capital density in an economy, etc.). Moreover, in contrast to many other suggested complexity measures, evaluating the self‐dissimilarity of a system does not require one to already have a model of the system. These facts may allow self‐dissimilarity signatures to be used as the underlying observational variables of an eventual overarching theory relating all complex systems. To illustrate self‐dissimilarity, we present several numerical experiments. In particular, we show that the underlying structure of the logistic map is picked out by the self‐dissimilarity signature of time series produced by that map. © 2007 Wiley Periodicals, Inc. Complexity 12: 77–85, 2007     

Guiding Teachers in the Use of a Standards‐Based Mathematics Curriculum: Teacher Perceptions and Subsequent Instructional Practices After an Intensive Professional Development Program

Reforms in mathematics education call for K‐12 teachers to employ standards‐based pedagogies, which embody the National Council for Teachers of Mathematics' principles and standards. In order to effectively support teachers' implementation of standards‐based curricula, professional development must be provided that meets teachers' needs. The professional development program in this study focused on the implementation of a standards‐based mathematics curriculum entitled Investigations in Number, Data, and Space (Investigations). This study uses Guskey's framework as a guide to examining teachers' perceptions of the impact of the professional development that they received; their perceptions of mathematics teaching and learning; and how elements of the professional development translated into practice. Twenty‐two participants were randomly selected from the 53 professional development participants to be interviewed and observed during their mathematics teaching. Using a constant comparison method, the data sources in this study highlighted themes surrounding teachers' experiences with professional development and the implementation of the curricula. The analysis of the data sources in this study highlighted themes surrounding teachers' experiences with professional development: teachers as learners, teachers as self‐evaluators, shifting paradigms, enactment of professional development content into practice, and the influence of the state standardized mathematics test. The results of this study have several implications for future professional development and also highlight some of the more general issues that teachers face when attempting to enact new knowledge and skills into their practice.