Showing papers in "School Science and Mathematics in 2007"
TL;DR: The authors investigated the mathematics beliefs and content knowledge of 103 elementary pre-service teachers in a developmental teacher preparation program that included a two course mathematics methods sequence and found that teachers' pedagogical beliefs became more cognitively-oriented during teacher preparation with these changes occurring during the two methods courses.
Abstract: This study investigated the mathematics beliefs and content knowledge of 103 elementary pre-service teachers in a developmental teacher preparation program that included a two course mathematics methods sequence. Pre-service teachers' pedagogical beliefs became more cognitively-oriented during the teacher preparation program with these changes occurring during the two methods courses. Pedagogical beliefs remained stable during student teaching. The pre-service teachers also significantly increased their personal efficacy for teaching mathematics throughout the program with these shifts occurring across both methods courses and into student teaching. Pedagogical beliefs and teaching efficacy beliefs were not related at the beginning of the program, but, in general, were positively related throughout the program. In addition, the pre-service teachers' pedagogical beliefs were positively related to their specialized content knowledge for teaching mathematics at the end of the program.
167 citations
TL;DR: This paper developed and employed a rubric to help understand 24 beginning secondary science teachers' pedagogical content knowledge (PCK), focusing on two categories: knowledge of student learning and knowledge of instructional strategies.
Abstract: While it is generally accepted that pedagogical content knowledge (PCK) is an essential knowledge base for science teachers, educational researchers are not clear on how it develops. Previous researchers have suggested that classroom practice may play a significant role. Therefore, it is important to look at beginning teachers' PCK and its development during the first years in the classroom. Using the pilot year data from a larger study, we developed and employed a rubric to help understand 24 beginning secondary science teachers ‘PCK, focusing on two categories: Knowledge of Student Learning and Knowledge of Instructional Strategies. The results of analysis did not show a statistically significant change between the groups, but when comparisons were made with all of the teachers, the category of Knowledge of Students Learning did significantly change. In this paper we report the results of the pilot year data, provide examples of how we employed the rubric to assess teachers’ PCK, and discuss how this study benefits understanding beginning teachers' PCK.
143 citations
TL;DR: In this article, the authors investigated the relationship between self-regulated learning, motivation, anxiety, attributions and achievement in mathematics and found significant contributions are made by motivation and anxiety on both test score and mathematics grade for fifth grade students.
Abstract: For this quantitative study, a total of n = 761 students (58.1% female) from selected fifth- and sixth-grade mathematics classrooms in Alabama were surveyed in order to investigate the relationships between self-regulated learning, motivation, anxiety, attributions and achievement in mathematics. Data analyses revealed that significant contributions are made by motivation and anxiety on both test score and mathematics grade for fifth grade students. Specific factors (e.g., self-efficacy, worry, other, and failure) were related to academic performance while failure attribution was significantly related to mathematics grade. As for sixth grade students, data analyses showed relationships exist between motivation, anxiety and academic performance with specific factors (i.e., self-efficacy, intrinsic value, and worry) significantly predicting both test score and mathematics grade for sixth graders. The findings underlie the importance of motivation and anxiety for students and how these constructs interact to facilitate self-regulation over the course of developing expertise in a domain, such as mathematics.
84 citations
TL;DR: This paper examined the beliefs of K-8 preservice teachers during a content methods course and found that teachers made decisions based on an external locus of control and harbored greater anxiety about teaching math as compared to teaching science.
Abstract: This study examines the beliefs of K-8 preservice teachers during a content methods course. The goals of this course included exposing the preservice teachers to student-centered instructional methods for math and science and encouraging the development of lessons that would integrate mathematics and science. Prior research suggested that one must consider preservice teachers' epistemic beliefs (Cady, Meier, & Lubinski, 2006a) as it influences their interpretation of the teacher education program. In this study, preservice teachers' epistemic beliefs were identified, their beliefs about mathematics and science teaching and learning were identified and compared, and their descriptions of lessons that integrated mathematics and science were assessed. Findings suggest that preservice teachers made decisions based on an external locus of control and harbored greater anxiety about teaching math as compared to teaching science. They also indicate that the integration of mathematics and science in lesson plans was contrived.
77 citations
TL;DR: The authors investigated students' understanding about scientifically acceptable content knowledge by exploring the relationship between knowledge of diffusion and osmosis and the student's certainty in their content knowledge, and found that significantly more students had misconceptions than desired knowledge on content covering the Influence of Life Forces on Diffusion and Osmosis, Membranes, the Particulate and Random Nature of Matter, and the Processes of Diffusion.
Abstract: The purpose of this study was to investigate students' understanding about scientifically acceptable content knowledge by exploring the relationship between knowledge of diffusion and osmosis and the student's certainty in their content knowledge. Data was collected from a high school biology class with the Diffusion and Osmosis Diagnostic Test (DODT) and Certainty of Response (CRI) scale. All data was collected after completion of a unit of study on diffusion and osmosis. The results of the DODT were dichotomized into correct and incorrect answers, and CRI values were dichotomized into certain and uncertain. Values were used to construct a series of 2 × 2 contingency tables for each item on the DODT and corresponding CRI. High certainty in incorrect answers on the DODT indicated tenacious misconceptions about diffusion and osmosis concepts. Low certainty in incorrect or correct answers on the DODT indicated possible guessing; and, therefore no understanding, or confusion about their understanding. Chi-square analyses revealed that significantly more students had misconceptions than desired knowledge on content covering the Influence of Life Forces on Diffusion and Osmosis, Membranes, the Particulate and Random Nature of Matter, and the Processes of Diffusion and Osmosis. Most students were either guessing or had misconceptions about every item related to the concepts osmosis and tonicity. Osmosis and diffusion are important to understanding fundamental biology concepts, but the concept of tonicity not be introduced to high school biology students until effective instructional approaches can be identified by researchers.
58 citations
TL;DR: In this paper, the authors examined the strategies used by pre-service teachers when answering number sense related questions and found that about one third of the teachers were able to use number sense strategies such as recognizing the number size, using benchmarks, etc.
Abstract: This study examined the strategies used by pre-service teachers when responding to number sense related questions. 15 pre-service teachers from one University in Southern Taiwan were interviewed. Results indicated that about one-third of these pre-service teachers were able to use number sense strategies (such as recognizing the number size, using benchmarks, etc.) and the other two-thirds relied heavily on written algorithms to solve problems. This is consistent with the findings of the earlier studies (Reys & Yang, 1998; Yang & Reys, 2002; Yang, 2003), which state that fifth, sixth and eighth graders in Taiwan rely heavily on the written method when responding to number sense related questions. This implies that the performance of pre-service elementary teachers on number sense is low. If we want to improve elementary students' knowledge and use of number sense, then we should try to improve the ability of their future teachers' number sense. This supports the statement of Ma (1999) which stated that “to empower students with mathematical thinking, teachers should first be empowered (p. 105).”
51 citations
TL;DR: In this paper, the authors examined the support structures and strategies utilized by beginning mathematics and science teachers and proposed a model of beginning teachers' initiating access to support structures based on the realization that their ideal images of teaching do not match the realities of their classrooms.
Abstract: This study examines the support structures and strategies utilized by beginning mathematics and science teachers. The qualitative case study of 18 teachers (0–3 years of experience) includes teachers from rural, suburban and urban schools. Data collection consisted of one-hour interviews. The findings indicate participants utilized formal and informal support structures within the school district (e.g., mentoring programs, talking to other new teachers) as well as those external to the school (e.g., professional organizations and conferences, talking to family and friends). We propose a model of beginning teachers' initiating access to support structures based on the realization that their ideal images of teaching do not match the realities of their classrooms. Implications are given for teacher educators, researchers, and school administrators.
46 citations
TL;DR: In this article, the authors describe a unique field assignment created for an Elementary Math Methods course in which 61 preservice teachers were trained to conduct a semi-structured interview with a student whose cultural background was different than their own.
Abstract: Teacher education programs are cognizant of the need to prepare preservice teachers (PTs) to work effectively with children from diverse cultural backgrounds. Well-constructedfield experiences can help PTs develop awareness and gain understanding of important cultural considerations related to effective teaching and learning (Sleeter, 2001). This paper describes a unique field assignment created for an Elementary Math Methods course in which 61 PTs were trained to conduct a semi-structured interview with a student whose cultural background was different than their own. PTs transcribed their own interviews and completed a guided reflection on their experiences. Reflections were submitted and analyzed for emerging themes. Analyses suggest that the structured interview component of this field assignment provided PTs with increased insight into mathematics instruction and the learning needs of diverse students. We also discuss the value and limitations of this instructional innovation and propose avenues by which to continue to help PTs grow toward becoming culturally relevant pedagogists (Irvine, 2003).
41 citations
TL;DR: The authors investigated K-12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction and found that high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction compared to elementary teachers.
Abstract: This study investigated K-12 teachers' beliefs and reported teaching practices regarding calculator use in their mathematics instruction. A survey was administered to more than 800 elementary, middle and high school teachers in a large metropolitan area to address the following questions: (a) what are the beliefs and practices of mathematics teachers regarding calculator use? and (b) how do these beliefs and practices differ among teachers in three grade bands? Factor analysis of 20 Likert scale items revealed four factors that accounted for 54% of the variance in the ratings. These factors were named Catalyst Beliefs, Teacher Knowledge, Crutch Beliefs, and Teacher Practices. Compared to elementary teachers, high school teachers were significantly higher in their perception of calculator use as a catalyst in mathematics instruction. However, the higher the grade level of the teacher, the higher the mean score on the perception that calculator use may be a way of getting answers without understanding mathematical processes. The mean scores for teachers in all three grade bands indicated agreement that students can learn mathematics through calculator use and using calculators in instruction will lead to better student understanding and make mathematics more interesting. The survey results shed light on teachers' self reported beliefs, knowledge, and practices in regard to consistency with elements of the National Council of Teachers of Mathematics Principles and Standards for School Mathematics (2000) technology principle and the NCTM use of technology position paper (2003). This study extended previous research on teachers' beliefs regarding calculator use in classrooms by examining and comparing the results of teacher surveys across three grade bands.
29 citations
27 citations
TL;DR: In this paper, a collaborative project between university graduate fellows and K-12 classroom teachers had an impact on improved pedagogy in the classroom and in the future at the university.
Abstract: This article focuses on the impact a collaborative project between university graduate fellows and K-12 classroom teachers had on improved pedagogy in the classroom and in the future at the university. Nine teams participated in a yearlong professional development project to improve pedagogy and communication skills of the participants. This study shows that the participants, the fellows and the K-12 teacher partners, made changes in planning, implementation, and even motivation for using inquiry-based methods in their classroom.
External observations of the teams further support the individuals' claims of improved pedagogy using inquiry and impact on student conceptual understanding. The Horizon Classroom Observation instrument was used for these observations. The teams showed an overall increase in scores, as well as overall effective and exemplarily implementation of their planning. The program design, the implementation, and the results of this three-year study will be elaborated in this article.
TL;DR: The authors describes the range of field investigations conducted by scientists and K-12 students and elaborates a comparative model of three different types of field investigation (descriptive studies, comparative studies, correlative studies).
Abstract: Field investigations are not characterized by randomized and manipulated control group experiments, however most school science and high-stakes tests recognize only this paradigm of investigation. Scientists in astronomy, genetics, field biology, oceanography, geology, and meteorology routinely select naturally occurring events and conditions and look for descriptive, correlative, or causal trends. Field investigations contribute to scientific knowledge by describing natural systems, noting differences in habitats, and identifying environmental trends and issues; they are designed to answer an investigative question through the systematic collection of evidence and the communication of results. This paper describes the range of field investigations conducted by scientists and K-12 students and elaborates a comparative model of three different types of field investigations (descriptive studies, comparative studies, correlative studies). These forms of investigation are more representative of current scientific practice and provide rigorous and engaging inquiry experiences for young learners.
TL;DR: Science Camp as discussed by the authors is a university day camp offering problem-based science exploration for urban middle school students and an introduction to college life, and for parents it is an opportunity to learn about college opportunities for their children and to gather information about funding sources.
Abstract: This paper reports on creative partnerships to create learning communities to benefit students, parents, and teachers in the urban setting. Science Camp is a university day camp offering problem-based science exploration for urban middle school students and an introduction to college life. For parents it is an opportunity to learn about college opportunities for their children and to gather information about funding sources. For middle school science teachers and preservice teachers it is a learning laboratory for conducting problem-based learning in the urban setting. The findings describe the effects of the learning communities on the transformation of students, parents, preservice teachers, and in-service teachers.
TL;DR: This article found that the equal sign misconception was still manifest in a U.S. sample and present in a Chinese sample and found that using the calculator reinforces the equal-sign misconception since the answer comes after the answer is pressed.
Abstract: Inferiors revolt in order that they may be equal; equals revolt in order that they may be superior (Aristotle, 322BC). Teachers and researchers have long recognized that students tend to misunderstand the equal sign as an operator, that is, a signal for \"doing something\" rather than a relational symbol of equivalence or quantity sameness (Behr, Erlwanger, & Nichols 1980; National Council of Teachers of Mathematics [NCTM], 2000; Sáenz-Ludlow & Walgamuth, 1998; Thompson & Babcock, 1978). Students' equal sign misconception has been researched for more than thirty years (Weaver, 1971,1973) with little refinement in the theory. It was popularly believed that younger students were not developmental ly ready to work variations of open numbers sentences, such as missing addend problems (Thompson & Babcock, 1978). In fact, misconceptions about the equal sign were identified in kindergarten students even before formal instruction (Falkner, Levi, & Carpenter, 1999). However, it is clear that with specific instructional guidance, elementary students can understand the equal sign expresses a relation (Baroody & Ginsburg, 1983; Carpenter, Levi, & Farnsworth, 2000; Saenz-Ludlow & Walgamuth, 1998). These previous studies did not employ random selection, examine the phenomenon internationally, or explore how materials used with elementary teachers prepare them to teach the equal sign. A major benefit of international comparisons is that cross-cultural comparisons lead to more explicit understanding of one's own implicit theories about how children learn mathematics (Stigler & Perry, 1988). We examined variables that could contribute to students' equivalence misconception and whether the 86 equal sign misconception was still manifest in a U.S. sample and present in a Chinese sample. First, six Ü. S. methods books were chosen and examined to determine what strategies were being presented to prepare U.S. elementary preservice teachers (PTs) to teach equivalence and the equal sign to their future students. Strategies ranged from nothing at all (Smith, 2001 ), to a single paragraph (Cathcart, Pothier, Vance, & Bezuk, 2006; Reys, Linquist, Lamdbin, Smith, & Suyday, 2004; Van de Walle, 2004), to an activity (Tucker, Singleton, & Weaver, 2006). Seemingly, the authors of these textbooks expect that PTs understand the issues related to the equal sign and the implications for their students. Both Reys et al. (2004) and Van de Walle (2004) alert PTs to the common misconception that the equal sign means \"the answer is next.\" Both authors dutifully inform readers that using the calculator reinforces the equal sign misconception since the answer comes after the equal sign is pressed. To counteract this misconception, a balance scale can help students develop the correct conceptual understanding of equality and the equal sign (Reys et al., 2004). Van de Walle (2004) suggests that teachers should use the phrase \"is the same as\" (p. 139) instead of \"equals\" as students read number sentences.
TL;DR: In this article, a phenomenological approach was used to investigate the longitudinal recollections of participants of an out-of-school science program in the Shenandoah National Park (USA) conducted in the fall of 2004.
Abstract: A phenomenological approach was used to investigate the longitudinal recollections of participants of an out-of-school science program. The experience was a field trip to the Shenandoah National Park (USA) conducted in the fall of 2004. The science topic was geologic history and features related to the Shenandoah Valley. Two major themes relating to the participants' long term recollection of the out-of-school science field trip were identified after the interview data was analyzed. First, recollections were highly influenced by actions taken by the students, and, second, program content / subject matter were retained by all of the students to varying degrees. The interactive experiences that aided in memory retrieval from this study closely relates to the interactive experiences associated with memory and learning theory associated with the psychological domain. This linkage and its impact on how students learn in out-of-school science experiences are discussed.
TL;DR: This article examined the role of gender in the areas of environmental education that included environmental knowledge, attitudes, behaviors, and comfort levels in the outdoors and found significance in boys' and girls' attitudes toward the environment.
Abstract: This study examined the role of gender in the areas of environmental education that included environmental knowledge, attitudes, behaviors, and comfort levels in the outdoors. The current study was part of a larger study designed to explore the effects of a treatment that consisted of 14 weeks of outdoor lessons conducted in the schoolyard as compared with a control group of students who had 14 weeks of traditional classroom environmental education lessons. This follow-up study focused on gender and its effect on each of the areas studied. Researchers found significance in boys' and girls' attitudes toward the environment. Quantitative and qualitative data were used to offer an in-depth view of students' environmental attitudes. The results from this study can have implications for science educators in an effort to capitalize on boys' and girls' interests in science to help them learn about environmental issues and to recruit both boys and girls into science careers.
TL;DR: In this paper, written assessment items were developed to probe students' understanding of a variety of direct current (DC) resistive electric circuit concepts, and the items were used to explore the mental models that grade 3-8 students use in explaining the direction of electric current and how electric current is affected by different configurations of simple battery and bulb circuits.
Abstract: Written assessment items were developed to probe students’ understanding of a variety of direct current (DC) resistive electric circuit concepts. The items were used to explore the mental models that grade 3–8 students use in explaining the direction of electric current and how electric current is affected by different configurations of simple battery and bulb circuits. Consistency of applying mental models in different, but equivalent, circuits was also analyzed. Students analyses of current flow direction was categorized into one of two mental models: (1) bidirectional and (2) unidirectional. We found an increase in the consistency of current flow direction mental model use coinciding with grade 4 instruction of batteries and bulbs, however, the proportion of students using a bidirectional flow model was similar in grades 3–8.
TL;DR: In this paper, the use of problem posing in the calculus classroom using investigative projects is explored, and four examples of student work are examined, each one differing in originality of problem posed.
Abstract: This article explores the use of problem posing in the calculus classroom using investigative projects. Specially, four examples of student work are examined, each one differing in originality of problem posed. By allowing students to explore actual questions that they have about calculus, coming from their own work or class discussion, or questions arising from studying supplementary material, all students can successfully engage in problem posing.
TL;DR: In this paper, the authors describe a professional development course intended to improve the content understanding of middle school mathematics teachers, which included three professional learning strategies: problem solving, examination of student thinking, and discussion of research.
Abstract: This article describes a professional development course intended to improve the content understanding of middle school mathematics teachers. The design of the course included three professional learning strategies: problem solving, examination of student thinking, and discussion of research. The concepts studied in the course included multi-digit subtraction, multi-digit multiplication, operations with fractions, and concepts of area and perimeter. Results from pre- and post-tests administered to the nineteen participants indicate a significant increase in the mean score for each concept and document growth in the teachers' content understanding. In particular, their solutions moved from primarily procedural to more conceptual. Responses to an open-ended survey indicate other important aspects of the professional development. Examples of teachers' work and comments are included.
TL;DR: The authors investigated a middle school mathematics teacher's reflection on her students while watching videotapes of her classroom and categorized the reflection as Assess, Interpret, Describe, Justify, and Extend.
Abstract: The purpose of this research was to understand how one teacher reflected on different classroom situations and to understand whether the teacher's approach to these reflections changed over time. For the purposes of this study, we considered reflection as the teacher's act of interpreting her own practices and students' thinking to make sense of student understanding and how teaching might relate to that understanding. We investigated a middle school mathematics teacher's reflection on her students while watching videotapes of her classroom and categorized the reflection as Assess, Interpret, Describe, Justify, and Extend. The results show a higher percentage of Extend instances in later interviews than in earlier ones indicating the teacher's increasing attention to her own teaching in how her students developed their understanding. In addition, her reflection became clearer and better integrated as defined by the Cohen and Ball's triangle of interactions.
TL;DR: This paper developed and established the validity and reliability of an instrument to measure students' attitudes toward geometry, which is a 5-point Likert-scaled survey consisting of 32 statements and three subscales.
Abstract: The purpose of this study was to develop and establish the validity and reliability of an instrument to measure students' attitudes toward geometry. Participants consisted of 264 undergraduate students from two universities, one in the Midwest and one in the Southwest. The instrument is a 5-point Likert-scaled survey consisting of 32 statements and 3 subscales. The internal consistency using Cronbach's coefficient alpha was 0.95 for the confidence subscale, 0.93 for the usefulness subscale, and 0.92 for the enjoyment subscale. For the overall instrument using the 32 items that comprised the three subscales, internal consistency reliability analysis revealed a Cronbach's coefficient alpha of 0.96. Additionally, this article reports on the content, criterion, and construct validity of the instrument.
TL;DR: This article investigated how students who had not been exposed to formal algebraic methods approached word problems of an algebraic nature, and found that the students' use of systematic guess and check reasoning in terms of the broadening perspective of algebra and algebraic thinking can provide a basis for developing some of the thinking patterns and discourse of formal algebra.
Abstract: This article will share results from research that investigated how sixth-, seventh-, and eighth-grade students who had not been exposed to formal algebraic methods approached word problems of an algebraic nature. Student use of systematic guess and check, the predominate approach taken by these students, is the focus. The goal is to consider the students' use of systematic guess and check reasoning in terms of the broadening perspective of algebra and algebraic thinking by highlighting ways in which this reasoning can provide a basis for developing some of the thinking patterns and discourse of formal algebra. Two perspectives will be highlighted: relationships among quantities and function-based reasoning.
TL;DR: In this article, a 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.
Abstract: 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
TL;DR: In this article, the alignment of the content of the developmental and college level mathematics courses was studied empirically at a medium sized public liberal arts university, and the results of such a study were used to serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and College-Level mathematics courses.
Abstract: Over one-third of all college mathematics enrollments are in courses considered to be developmental. While such courses have been the subject of a large body of research, one question that seems not to have been studied empirically is the alignment of the content of developmental and college level mathematics courses. This paper gives the results of such a study, conducted at a medium sized public liberal arts university. While the content of the developmental mathematics courses was used subsequently in the Precalculus course, most of the content of the Intermediate Algebra course was not used in other college level mathematics courses. It is hoped that the results of this paper will serve as a catalyst for other institutions to examine carefully and define the mission of both their developmental and college level mathematics courses.