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Showing papers in "School Science and Mathematics in 2008"


Journal ArticleDOI
TL;DR: In this article, a collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K-8) involved in lesson study as part of a professional development program.
Abstract: This collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K-8) involved in lesson study as part of a professional development program. The study found that in three of four lessons studied manipulative use was turned into an end in and of itself, rather than a tool, and that in the fourth lesson manipulative use hindered rather than helped student learning. These problems with manipulative use by teachers in the lessons provide helpful guidance for planning of future professional development for math teaching. Our conclusion contains recommendations for successful implementation of manipulatives for both teachers and professional developers. Most importantly, we stress the need to emphasize the link between pedagogy and content, not the specific use of manipulatives.

75 citations


Journal ArticleDOI
TL;DR: This article assessed the influence of using mind maps as a learning tool on eighth graders' science achievement, whether such influence was mediated by students' prior scholastic achievement, and the relationship between students' mind maps and their conceptual understandings.
Abstract: This study assessed the influence of using mind maps as a learning tool on eighth graders’ science achievement, whether such influence was mediated by students’ prior scholastic achievement, and the relationship between students’ mind maps and their conceptual understandings. Sixty-two students enrolled in four intact sections of a grade 8 science classroom were randomly assigned to experimental and comparison conditions. Participants in the experimental group received training in, and constructed, mind maps throughout a science unit. Engagement with mind mapping was counterbalanced with involving the comparison group participants with note summarization to control for time on task as a confounding variable. Otherwise, the intervention was similar for both groups in all respects. A multiple choice test was used to measure student gains across two categories and three levels of achievement. Data analyses indicated that the experimental group participants achieved statistically significant and substantially higher gains than students in the comparison group. The gains were not mediated by participants’ prior scholastic achievement. Analyses also indicated that iconography was not as central to participants’ mind maps as often theorized. Depicting accurate links between central themes and major and minor concepts, and using colors to represent concepts were the major aspects that differentiated the mind maps built by students who achieved higher levels of conceptual understanding.

74 citations


Journal ArticleDOI
TL;DR: For example, the authors investigated how fourth and fifth grade students spontaneously packed a word problem when generating a graphic representation to aid in problem solving and found that the majority of students rendered schematic representations, with girls more likely than boys to use schematic representations at a statistically significant level.
Abstract: This research investigated how fourth and fifth grade students spontaneously ‘unpacked’ a word problem when generating a graphic representation to aid in problem solution. Relationships among the type of graphic representation produced, spatial visualization, drawing ability, gender, and problem solving also were examined and described. Instrumentation developed for the study included several math challenge tasks, a spatial visualization task, and a drawing task. For one of the math challenge tasks, students were instructed to draw a picture to assist them with problem solution. These graphic representations generated by students were rated as pictorial or as displaying some level of schematic representation. Schematic representations included germane information from the problem supportive of problem solution. Pictorial representations included expressive and extraneous elements not necessary for problem solution, with no schematic elements. Findings indicated that the majority of students rendered schematic representations, with girls more likely than boys to use schematic representations at a statistically significant level. Students who used schematic visual representations were more successful problem solvers than those pictorially representing problem elements. The more “schematic-like” the visual representation, the more successful students were at problem solution. Drawing a pictorial representation in the math challenge task also was negatively correlated to drawing skill.

66 citations


Journal ArticleDOI
TL;DR: There is a variety of technologies integrated into mathematics classrooms that support different teaching and learning strategies and objectives as mentioned in this paper. But, the most common technologies used in K-12 mathematics classrooms and their effects on instruction and student learning are calculators.
Abstract: Technology integration in mathematics classrooms is important to the field of education, not only because today's society is becoming more and more advanced and reliant upon technology but also because schools are beginning to embrace technology as an essential part of their curricula. The Principles and Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 2000) and the National Educational Technology Standards (International Society of Technology in Education [ISTE], 2005) for both teachers and students emphasize the importance of technology in teaching and learning for K-12. There is a variety of technologies integrated into mathematics classrooms that support different teaching and learning strategies and objectives. Of particular interest here are the educational technologies used in K-12 mathematics classrooms and their effects on instruction and student learning. Educational Technologies Used in Mathematics Classrooms Calculators. Calculators are one of the essential' technologies in mathematics classrooms that enhance student understanding (NCTM, 2000). Specifically, graphing calculators provide students and teachers with comprehensive ways to investigate, explore, and discover concepts (Harskamp, Suhre, & Van Streun, 2000). Graphing calculators are more prevalent in high schools (Dion, Harvey, Jackson, Klag, Liu, & Wright, 2001), and their use promotes deeper conceptual understanding by exposing students to multiple representations of mathematical concepts (Doerr & Zangor, 2000; Smith, 1998). Using calculators increases students' higher-order thinking skills and motivation (Phillips-Bey, 2004). These cumulative effects have been interpreted as helping to create an enhanced understanding of mathematics. Interactive Whiteboard While blackboards or whiteboards are universally used in every classroom, they are being replaced with interactive whiteboards. This

52 citations


Journal ArticleDOI
TL;DR: In this article, the authors discuss the differences and interrelations between statistics and mathematics, recognizing that mathematics is the discipline that has traditionally included instruction in statistics and conclude with an argument that statistics should be viewed as a bridge between mathematics and science and should be taught in both disciplines.
Abstract: Increasing attention has been given over the last decade by the statistics, mathematics and science education communities to the development of statistical literacy and numeracy skills of all citizens and the enhancement of statistics education at all levels This paper introduces the emerging discipline of statistics education and considers its role in the development of these important skills The paper begins with information on the growing importance of statistics in today's society, schools and colleges, summarizes unique challenges students face as they learn statistics, and makes a case for the importance of collaboration between mathematicians and statisticians in preparing teachers to teach students how to understand and reason about data We discuss the differences and interrelations between statistics and mathematics, recognizing that mathematics is the discipline that has traditionally included instruction in statistics We conclude with an argument that statistics should be viewed as a bridge between mathematics and science and should be taught in both disciplines

52 citations


Journal ArticleDOI
TL;DR: The authors explored the emerging blogging practices of one high school mathematics teacher and his class to explore issues of intent, use, and perceived value, finding that teachers' intentions focused on creating additional forms of participation as well as increasing student exposure time with content; and both teacher and students perceived the greater investment to be worthwhile.
Abstract: The challenge many teachers face is how to incorporate new technology into their classrooms that strengthens classroom learning by capitalizing on students’ media literacies. Blogs, a new and innovative technological tool, can be used in math and science classrooms to support student learning by capitalizing on students’ interests and familiarity with on-line communication. This study explores the emerging blogging practices of one high school mathematics teacher and his class to explore issues of intent, use, and perceived value. Data sources for this case included one year's worth of blog content, an interview with the facilitating teacher, and students ‘perceptions of classroom blogging practices. Findings indicate that (1) teachers’ intentions focused on creating additional forms of participation as well as increasing student exposure time with content; (2) blogs were used in a wide variety of ways that likely afforded particular benefits; and (3) both teacher and students perceived the greater investment to be worthwhile. The findings are used to critically consider claims made in the literature about the potential of blogging to effectively support classroom learning.

52 citations


Journal ArticleDOI
TL;DR: This article reported on an exploratory study of the mathematical beliefs of a group of ninth and tenth grade students at a large, college preparatory, private school in the Southeastern United States.
Abstract: This paper reports on an exploratory study of the mathematical beliefs of a group of ninth and tenth grade students at a large, college preparatory, private school in the Southeastern United States. These beliefs were revealed using contemporary metaphor theory. A thematic analysis of the students' metaphors for mathematics indicated that students had well developed and complex views about mathematics including math as: an Interconnected Structure, a Hierarchical Structure, a Journey of Discovery, an Uncertain Journey, and a Tool. Another prevalent theme revealed by the metaphors was that students believe perseverance is needed for success in mathematics. The data also suggest an impact of gender and tracking on students beliefs about mathematics. Creating metaphors for mathematics provided a catalyst for student reflection, class discussion, and qualitative data, which could aid program evaluation. Several areas for future research were identified through this exploratory study.

47 citations


Journal ArticleDOI
TL;DR: This article explored the vital role of purposeful reading and writing in the mathematics classroom and outlined some techniques to promote successful integration of reading and learning in mathematics, and found that students learn mathematics more effectively and more deeply when reading-and-writing is directed at learning mathematics.
Abstract: Students learn mathematics more effectively and more deeply when reading and writing is directed at learning mathematics Although reading and writing in mathematics may necessitate more skills and practice to master, the mathematical learning derived from reading and writing mathematics far outweighs the burden it places on teachers and students This paper explores the vital role of purposeful reading and writing in the mathematics classroom and outlines some techniques to promote successful integration of reading and writing in mathematics

42 citations


Journal ArticleDOI
TL;DR: Across the groups, participants were most knowledgeable about symptoms of microbial illness, treatments of symptoms, and routes of transmission for respiratory illnesses, but there were typically large gaps in participants' understandings of vaccines, immune system responses, treatments, and transmission of non-respiratory microbial illness.
Abstract: This study describes 5 th, 8th, and 11th-grade students', teachers', and medical professionals' conceptions of flu and microbial illness. Participants constructed a concept map on “flu” and participated in a semi-structured interview. The results showed that these groups of students, teachers and medical professionals held and structured their conceptions about microbes differently. A progression toward more accurate and complete knowledge existed across the groups but this trajectory was not always a predictable, linear developmental path from novice to expert. Across the groups, participants were most knowledgeable about symptoms of microbial illness, treatments of symptoms, and routes of transmission for respiratory illnesses. This knowledge was tightly linked to participants' prior experiences with colds and flu. There were typically large gaps in participants' (children and teachers) understandings of vaccines, immune system responses, treatments (including the mechanisms of pain medications and the functions of antibiotics), and transmission of non-respiratory microbial illness. A common misconception held by students was the belief that antibiotics can cure viral infections.

42 citations


Journal ArticleDOI
TL;DR: In this paper, a draw an engineer test was used to capture the perceptions of engineering held by two similar groups of 6th grade African-American students, using perceptions of common engineering artifacts, fields, tasks and processes as measures.
Abstract: A Draw an Engineer Test was used to capture the perceptions of engineering held by two similar groups of 6th grade African-American students. Forty-four students who had graduate level engineers in their classrooms during a prior school year as part of a GK-12 project were matched to 44 students who had not. Matching criteria included race, gender, and academic standing. Using perceptions of common engineering artifacts, fields, tasks and processes as measures, student perceptions were quantified using a Draw an Engineer Test Scoring Guide. Additional descriptive analysis was also conducted. Control group students’ perceptions centered on engineering as physical work and portrayed engineers primarily in construction or building trades. Experimental group students were more likely to perceive engineering as involving mental tasks such as designing, presenting and experimenting. Experimental group students also displayed greater awareness and understanding of various engineering fields.

40 citations


Journal ArticleDOI
TL;DR: This article investigated how well 381 prospective elementary, early childhood, and special education majors solved four arithmetic problems that required using the order of operations and found that fewer than half the subjects answered more than two questions correctly.
Abstract: This study investigates how well 381 prospective elementary, early childhood, and special education majors solved four arithmetic problems that required using the order of operations. Self-reported data show these students to be relatively able mathematically and confident in their ability, with no substantial dislike of mathematics. The percentage of answers that were incorrectthat is attributable to order of operations ranged from 21.7% to 78.5%. Overall, fewer than half the subjects answered more than two questions correctly. Of those subjects who performed multiplication before addition, which indicates some knowledge of order of operations, 30.9% performed addition before subtraction and 38.0% performed multiplication before division rather than from left to right, which suggests that instead of using the correct order of operations, these students used the common mnemonic PEMDAS or “Please excuse my dear Aunt Sally “literally, performing multiplicationbefore division and performing addition before subtraction, rather than from left-to-right. Furthermore, 78.5% of subjects used the incorrect order of operations to compute −32.

Journal ArticleDOI
TL;DR: In this paper, the impact of a service-learning experience on pre-service teachers' confidence and preparation in the area of mathematics was examined. And the authors found that as a result of the service learning experience, teachers noted increased understanding, innovation and confidence.
Abstract: In spite of repeated reform efforts, there is research and data that suggest that teachers lack the needed knowledge to successfully teach elementary mathematics. Some argue that teachers lack the needed content knowledge while other argue that a lack of confidence and practice are impacting teachers’ ability to successful teach mathematics. As a result of these issues, this paper looks at the impact of a service-learning experience on pre-service teachers’ confidence and preparation in the area of mathematics. The service-learning experience had a number of intended and unintended outcomes. As a result of the service-learning experience, pre-service teachers noted increased understanding, innovation and confidence in the area of mathematics.

Journal ArticleDOI
TL;DR: The Teaching Science as Inquiry (TSI) instrument as mentioned in this paper is an instrument designed to measure the self-efficacy beliefs of preservice teachers in regards to the teaching of science as inquiry.
Abstract: The purpose of this study was to further develop and validate the Teaching Science as Inquiry (TSI) Instrument, an instrument designed to measure the self-efficacy beliefs of preservice teachers in regards to the teaching of science as inquiry Based on the validation processes and the associated data analysis, the TSI demonstrates continued content and construct validity with high internal reliability when used with prospective elementary science teachers


Journal ArticleDOI
TL;DR: In this paper, the authors explored gender differences in mathematics achievement as demonstrated by performance on the mathematics subsection of a nationwide high school entrance examination in Turkey and concluded that socio-economic development of the regions was not a critical factor for gender differences.
Abstract: The purpose of this study was to explore gender differences in mathematics achievement as demonstrated by performance on the mathematics subsection of a nationwide high school entrance examination in Turkey. In this study, the cities in Turkey were separated into five groups according to their level of economic development. The analysis was based on 2647 students that were randomly selected from these five different groups of cities. Although results indicated a statistically significant difference in mathematics achievement in favor of cities with the highest economic status, the effect size was quite small, which indicates the difference was not practically significant. Results also showed the effect sizes for gender differences in mathematics achievement were very small in all groups of cities. It was concluded that socio-economic development of the regions was not a critical factor for gender differences in mathematics achievement.



Journal ArticleDOI
TL;DR: In this paper, a teacher development experiment was conducted to discover how to improve preservice teachers' abilities and attitudes toward using writing in mathematics, and the results indicated that writing is valuable to instruction and would include it in their teaching.
Abstract: “Math was strictly math, from what I remember.” This is a comment about using writing in mathematics from a preservice elementary teacher enrolled in a methods course. Comments such as these concern teacher educators who wish to prepare elementary teachers to include writing in mathematics instruction. A teacher development experiment was completed to discover how to improve preservice teachers’ abilities and attitudes toward using writing in mathematics. The preservice teachers made use of a graphic organizer to facilitate writing in the college math methods class, then practiced teaching writing with the same graphic organizer and in the math classes in an elementary classroom. Reflections of the preservice teachers illustrated this was a positive practice. The preservice teachers also concluded that writing in mathematics is valuable to instruction and would include it in their teaching.

Journal ArticleDOI
TL;DR: In this article, a 5-point Likert-type survey was designed to measure K-8 mathematics teachers' perceptions of their use of dialogic, univocal and general discourse in their classes.
Abstract: This article documents the development and use of a survey instrument designed to measure K-8 mathematics teachers ‘perceptions about discourse in mathematics classes. In particular, the 5-point Likert-type survey sought to address teachers ‘perceptions of their use of dialogic (dialogue to construct new meaning), univocal (conveying information), and general discourse in their mathematics classes. Factor analysis revealed three reliable factors that were compatible with the original constructs, these include: dialogic discourse (α3= .67), univocal discourse (α1= .83), and general discourse (α2= .68). These results suggest a framework that could be used to uncover K-8 teachers' perceptions of their use of discourse in mathematics instruction, especially if there is interest in tendencies toward univocal or dialogic discourse. In addition to research implications, the survey could be used to inform the design and implementation of teacher professional development that focuses on discourse in mathematics instruction.

Journal ArticleDOI
TL;DR: The authors examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP) and found that the teachers prepared by this program used slightly more reform-oriented instructional practices than those who were not prepared by it.
Abstract: This study examined the science and mathematics instruction of teachers who were initially prepared by the Collaboratives for Excellence in Teacher Preparation program (CETP). The focus of this study was on examining the extent to which science and mathematics teachers used more reform-oriented instructional practices in their classes when they entered the teaching profession. Data were gathered from twelve different CETP projects across the United States. A quasi-experimental design was used where science and mathematics teachers who were initially prepared by the CETP program were followed into the field and compared to teachers who were not prepared by the CETP program. The results indicate that the teachers prepared by the CETP program used slightly more reform-oriented instructional practices than teachers who were not prepared by the CETP program, although both mathematics and science teachers reported low levels of reform-oriented instruction. Implications of results for large-scale reform of science and mathematics teacher preparation are discussed.

Journal ArticleDOI
TL;DR: This article examined students' perceptions about gender and the subject of mathematics, as well as gender and mathematics learning and found that female secondary school students hold beliefs in gender neutrality more strongly than female pre-service teachers and that both males and females see differences in the way boys and girls act and are treated in mathematics classes.
Abstract: This study examined students’ perceptions about gender and the subject of mathematics, as well as gender and mathematics learning. Secondary school students and pre-service elementary teachers were surveyed using the Mathematics as a Gendered Domain and Who and Mathematics instruments developed by Leder and Forgasz (Leder, 2001). The data indicate that, similar to findings from the 1970s, students believe that mathematics is gender neutral, although females hold this belief more strongly than males. Female secondary school students hold beliefs in gender neutrality more strongly than female pre-service teachers. Data for secondary school students indicate that both males and females see differences in the way boys and girls act and are treated in mathematics classes (e.g., boys cause more distractions while girls care more about doing well). The data also show that secondary school males who believe they are good mathematics students tend to have more gender-neutral perceptions than those who believe they are average or below average. No such pattern appears for secondary school females.

Journal ArticleDOI
TL;DR: This paper examined teachers' changing definitions of inquiry over a semester using the process of guided reflection and found that conscious consideration of what inquiry means assisted teachers in broadening their perceptions of inquiry in four distinct aspects: inquiry is a coherent process consisting of particular actions, inquiry exists on a continuum, the goal of inquiry is science conceptual development, and inquiry provides a context for building connections between those engaged in inquiry, science and other content areas, and science and life.
Abstract: What is inquiry? Although many teachers are using inquiry based curricula, often they have not engaged in answering or personalizing this question. This study examined teachers' changing definitions of inquiry over a semester using the process of guided reflection. Through inquiry experiences and reflection, these teachers developed and communicated a more sophisticated understanding of inquiry. The findings suggest that conscious consideration of what inquiry means assisted teachers in broadening their perceptions of inquiry in four distinct aspects: 1) inquiry is a coherent process consisting of particular actions, 2) inquiry exists on a continuum, 3) the goal of inquiry is science conceptual development, and 4) inquiry provides a context for building connections between those engaged in inquiry, science and other content areas, and science and life.

Journal ArticleDOI
TL;DR: For instance, this article found that teachers relied heavily on curriculum materials for their test items, and these items tended to only assess students ability to recall basic facts or perform straightforward procedures, and the presence of a state test did not entice teachers to assess students at higher depth of knowledge levels.
Abstract: Classroom tests from nine eighth-grade mathematics teachers were collected from the 2003–04 and 2005–06 school years. These years represent one school year prior to the eighth-grade Ohio Achievement Test (OAT) in mathematics being implemented and the year after the eighth-grade OAT in mathematics was implemented, respectively. In addition, teachers were interviewed to determine factors that influence classroom assessment practices. Classroom assessment data were compared between the two years, and interview data were examined, to investigate the impact that the new state test was having on classroom assessment practices. An average of 87% of teachers' classroom assessment items were at the lowest depth of knowledge level during both years. Teachers relied heavily on curriculum materials for their test items, and these items tended to only assess students ability to recall basic facts or perform straightforward procedures. The presence of a state test did not entice teachers to assess students at higher depth of knowledge levels.

Journal ArticleDOI
TL;DR: In this article, a study of six middle school science teachers' beliefs and instructional practice about the coherence of the science they teach as articulated by National Science Education Standards (NRC, 1996) is presented.
Abstract: This article is about an investigation of six middle school science teachers’ beliefs and instructional practice about the coherence of the science they teach as articulated by National Science Education Standards (NRC, 1996). Many well intentioned reform efforts focus on improving content knowledge of teachers, but many classroom teachers regularly miss opportunities to provide conceptual connections within the science ideas building the sense of coherence in science. This investigation involved a quasi experimental study to examine the efficacy of a method for collecting data about middle school science teachers’ thinking about science and to determine if they teach science coherently. The teachers were surveyed, interviewed, provided concept maps about their thinking of the science they taught, and observed to investigate whether their practice reflects their beliefs. An examination of the teachers’ beliefs, stated and unstated curriculum, the connections among topics and the nature of science revealed that one, the observation tool may have merit for identifying the content and connections among science topics, and two, that teachers ‘stated beliefs consistent with the National Science Education Standards’ vision for coherent science, did not match their demonstrated practice. The content taught could be characterized in three ways; coherent content and few connections, coherent content and connections, and not coherent content. This indicates for this group of middle school science teachers that knowing how they think about science and how those beliefs are reflected in their teaching is complex. This study can inform teacher education and professional development efforts about the need to move beyond just content enhancement to examine prior beliefs about the connections of concepts within science.

Journal ArticleDOI
TL;DR: In this article, a cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems.
Abstract: A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are TIMSS items (a linear inequality and an equation involving square roots). The other problem involves square roots. We found that the majority of student pairs used symbol manipulation when solving the problems, and while many students seemed to prefer symbolic over graphical and tabular representations in their first attempt at solving the problems, we found that it was common for student pairs to use more than one strategy throughout the course of their solving. Students' use of graphing calculators to solve the problems is discussed.

Journal ArticleDOI
TL;DR: David's understandings of functions and periodicity were explored, through clinical interviews and contextualized through classroom observations as mentioned in this paper, through a study of David, a senior enrolled in a high school precalculus course.
Abstract: This is a study of David, a senior enrolled in a high school precalculus course. David's understandings of functions and periodicity was explored, through clinical interviews and contextualized through classroom observations. Although David's precalculus class was traditional, his understanding of periodic functions was unconventional. David engaged in sense making behaviors even though these behaviors were not encouraged or explicitly taught. A careful analysis of his work revealed that David's understandings of functions, function notation, and periodicity were compartmentalized. However, David was able to skirt compartmentalization through flexibility in problem solving, translation between representations, and transfer of mathematical information from one representation to another.

Journal ArticleDOI
TL;DR: The authors examined average-, high-and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations and found that top performing students scored significantly higher in problem solving.
Abstract: This study examined average-, high- and top-performing US fourth graders' rational number problem solving and their understanding of rational number representations. In phase one, all students completed a written test designed to tap their skills for multiplication, division and rational number word-problem solving. In phase two, a subset of students sorted cards that showed part-whole, ratio, quotient, measure, and operator perspectives of rational number representations. Each perspective was shown in numerical notational, word-problem, and visual formats. The results indicated that top-performing students scored significantly higher in problem solving and showed more effectively linked rational number representations than the other groups. The results imply that successful rational number problem solving is intertwined with representational knowledge for a wide range of rational numbers and that the bulk of US students do not possess effective skills for working with rational number representations.

Journal ArticleDOI
TL;DR: In this article, the authors describe preservice elementary teachers' reactions to Liping Ma's book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities, and summarize how reading and reflecting on KTEM gives preserve teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually.
Abstract: In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually.

Journal ArticleDOI
TL;DR: The authors found that low achieving grade 7 and 8 students who received support consisting of placement on a learning continuum, instruction focused on their specific learning needs, and concrete materials to represent mathematical constructs, benefited from teaching that emphasized construction over transmission of knowledge.
Abstract: Previous research (e.g., Woodward & Baxter, 1997) found that Standards-based mathematics teaching provides marginal or no benefits for low achievers, in contrast with positive effects for middle and high ability students. A randomized quasi-experiment in 52 Canadian schools found that low achieving grade 7 and 8 students who received support consisting of placement on a learning continuum, instruction focused on their specific learning needs, and concrete materials to represent mathematical constructs, benefited from teaching that emphasized construction over transmission of knowledge. Treatment students showed small but statistically significant improvements over controls in student achievement, and controversially, in mathematical beliefs, and attitudes. The latter finding raised issues of the appropriate balance between Type I and Type II error in educational research.

Journal ArticleDOI
TL;DR: The authors argue that teachers' reflection on their teaching can cause them to recognize and validate their students' ways of knowing as they identify the students' hidden/concealed abilities that are often masked by their behaviors.
Abstract: Three mathematics and science educators reexamine and reflect on their teaching within the context of the American Association for the Advancement of Sciences (AAAS) and National Council of Mathematics' call to make math and science education accessible to all. The paper highlights the importance of teachers reflecting on their teaching practices in order to create opportunities for their students especially those in the urban setting. The educators argue that teachers' reflection on their teaching can cause them to recognize and validate their students' ways of knowing as they identify the students' hidden/concealed abilities that are often masked by their behaviors. The educators discuss their experiences and highlight the lessons that they learned about ways to prepare teachers to successfully teach math and science students in urban settings. Culturally responsive pedagogy and cultural competency are critical skills that teachers need to develop in order to teach all children, especially those in the math and science classroom in the urban setting.