Development of a Geometric Spatial Visualization Tool

This paper documents the development of the Geometric Spatial Assessment. We detail the development of this instrument which was designed to identify middle school students' strategies and advancement in understanding of four geometric concept domains (geometric spatial visualization, spatial projection, cardinal directions, and periodic patterns) after experiencing a carefully designed integrated lunar unit. Previous research with students using this lunar unit showed students making significant gains on lunar‐related concepts (both scientific and mathematical) on a Lunar Phases Concept Inventory (LPCI) ( Lindell & Olsen, 2002 ). Following the administration of single domain assessments, clinical interviews were conducted to ascertain students' problem solving strategies. Results allowed us to select four suitable multiple‐choice items per domain.     

Gender Differences in Learning Constructs,Shifts in Learning Constructs,and Their Relationship to Course Achievement in a Structured Inquiry,Yearlong College Physics Course for Life Science Majors

This study investigated differences and shifts in learning and motivation constructs among male and female students in a nonmajors, yearlong structured inquiry college physics course and examined how these variables were related to physics understanding and course achievement. Tests and questionnaires measured students' learning approaches, motivational goals, self‐efficacy, epistemological beliefs, scientific reasoning abilities, and understanding of central physics concepts at the beginning and end of the course. Course achievement scores were also obtained. The findings showed that male students had significantly higher self‐efficacy, performance goals, and physics understanding compared to females, which persisted throughout the course. Differential shifts were found in students' meaningful learning approaches, with females tending to use less meaningful learning from beginning to end of the course; and males using more meaningful learning over this time period. For both males and females, self‐efficacy significantly predicted physics understanding and course achievement. For females, higher reasoning ability was also a significant predictor of understanding and achievement; whereas for males, learning goals and rote learning were significant predictors, but in a negative direction. The findings reveal that different variables of learning and motivation may be important for females' success in inquiry physics compared to males. Instructors should be cognizant of those needs in order to best help all students learn and achieve in college physics.     

Students' Understanding of the Particulate Nature of Matter

The particulate nature of matter is identified in science education standards as one of the fundamental concepts that students should understand at the middle school level. However, science education research in indicates that secondary school students have difficulties understanding the structure of matter. The purpose of the study is to describe how engaging in an extended project‐based unit developed urban middle school students' understanding of the particulate nature of matter. Multiple sources of data were collected, including pre‐ and posttests, interviews, students' drawings, and video recordings of classroom activities. One teacher and her five classes were chosen for an indepth study. Analyses of data show that after experiencing a series of learning activities the majority of students acquired substantial content knowledge. Additionally, the finding indicates that students' understanding of the particulate nature of matter improved over time and that they retained and even reinforced their understanding after applying the concept. Discussions of the design features of curriculum and the teacher's use of multiple representations might provide insights into the effectiveness of learning activities in the unit.     

The Contribution of Conceptual Change Texts Accompanied by Concept Mapping to Students' Understanding of the Human Circulatory System

The present study was conducted to investigate the contribution of conceptual change texts accompanied by concept mapping instruction to 10^th— grade students' understanding of the human circulatory system. To determine misconceptions concerning the human circulatory system, 10 eleventh-grade students were interviewed. In the light of the findings obtained from student interviews and related literature, the Human Circulatory System Concepts Test was developed. The data were obtained from 26 students in the experimental group taught with the conceptual change texts accompanied by concept mapping, and 23 students in the control group taught with the traditional instruction. Besides treatment, previous learning in biology and science process skills were other independent variables involved in this study. Multiple Regression Correlation analysis revealed that science process skill, the treatment, and previous learning in biology each made a statistically significant contribution to the variation in students' understanding of the human circulatory system. It was found that the conceptual change texts accompanied by concept mapping instruction produced a positive effect on students' understanding of concepts. The mean scores of experimental and control groups showed that students in the experimental group performed better with respect to the human circulatory system. Item analysis was carried out to determine and compare the proportion of correct responses and misconceptions of students in both groups. The average percent of correct responses of the experimental group was 59.8%, and that of the control group was 51.6% after treatment.     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

The Effects of a Mathematics Infusion Curriculum on Middle School Student Mathematics Achievement

Increasing mathematical competencies of American students has been a focus for educators, researchers, and policy makers alike. One purported approach to increase student learning is through connecting mathematics and science curricula. Yet there is a lack of research examining the impact of making these connections. The Mathematics Infusion into Science Project, funded by the National Science Foundation, developed a middle school mathematics‐infused science curriculum. Twenty teachers utilized this curriculum with over 1,200 students. The current research evaluated the effects of this curriculum on students' mathematics learning and compared effects to students who did not receive the curriculum. Students who were taught the infusion curriculum showed a significant increase in mathematical content scores when compared with the control students.     

The Effects of a STEM Intervention on Elementary Students' Science Knowledge and Skills

The purpose of the study was to assess elementary students' science process skills, content knowledge, and concept knowledge after one year of participation in an elementary Science, Technology, Engineering, and Mathematics (STEM) program. This study documented the effects of the combination of intensive professional development and the use of inquiry‐based science instruction in the elementary classroom, including the benefits of using rigorous science curriculum with general education students. The results of the study revealed a statistically significant gain in science process skills, science concepts, and science‐content knowledge by general education students in the experimental group when compared with students in the comparison group. Moreover, teacher participation in the STEM program had a statistically significant impact on students' variability in posttest scores. These interim student performance data support the implementation of rigorous differentiated science curriculum focused on improving science concept, content knowledge, and process skills.     

Investigating High School Students' Science Experiences and Mechanics Understanding

This research study was designed to provide an introductory examination of how high school students' out‐of‐school science experiences, particularly those relevant to the physical sciences, relate to their learning of Newtonian mechanics. A factor analysis of the modified Science Experiences Survey (SES; Mason & Kahle, 1988 ) was performed, leading to three factors: Learning Attributes Related to Science, Physical Science Experiences, Nature Experiences. The students' learning of Newtonian mechanics was measured by their gain score from a pre‐instruction/post‐instruction administration of the Force Concept Inventory (FCI; Hestenes, Wells, & Swackhamer, 1992 ). An analysis of variance showed that females and males in honors physics courses demonstrated similar gain scores, while males in non‐honors courses demonstrated larger gains (p < 0.05) than the females. When the students' total SES and SES factor scores were correlated with their FCI pretest and gain scores, the SES Physical Science Experience score was found to be significantly related to the FCI pretest score (p = 0.01). No other correlations were significant.     

Students' Concepts‐ and Theorems‐in‐Action on a Novel Task About Similarity

Similarity is a fundamental concept in the middle grades. In this study, we applied Vergnaud's theory of conceptual fields to answer the following questions: What concepts‐in‐action and theorems‐in‐action about similarity surfaced when students worked in a novel task that required them to enlarge a puzzle piece? How did students use geometric and multiplicative reasoning at the same time in order to construct similar figures? We found that students used concepts of scaling and proportional reasoning, as well as the concept of circle and theorems about similar triangles, in their work on the problem. Students relied not only on visual perception, but also on numeric reasoning. Moreover, students' use of multiplicative and proportional concepts supported their geometric constructions. Knowledge of the concepts and ideas that students have available when working on a task about similarity can inform instruction by helping to ground formal introduction of new concepts in students' informal prior experiences and knowledge.     

Students' Attitudes Toward Science as Predictors of Gains on Student Content Knowledge: Benefits of an After‐School Program

High‐quality after‐school programs devoted to science have the potential to enhance students' science knowledge and attitudes, which may impact their decisions about pursuing science‐related careers. Because of the unique nature of these informal learning environments, an understanding of the relationships among aspects of students' content knowledge acquisition and attitudes toward science may aid in the development of effective science‐related interventions. We investigated the impact of a semester‐long after‐school intervention utilizing an inquiry‐based infectious diseases curriculum (designed for use after‐school) on 63 urban students' content knowledge and aspects of their attitudes toward science. Content knowledge increased 24.6% from pretest to posttest. Multiple regression analyses indicated suggested that the “self‐directed effort” subscale of the Simpson–Troost Attitude Questionnaire—Revised best predicted increases in students' science content knowledge. The construct “science is fun for me” served as a suppressor effect. These findings suggest that future after‐school programs focusing on aspects of attitudes toward science most closely associated with gains in content knowledge might improve students' enthusiasm and academic preparedness for additional science coursework by improving student attitudes toward their perceptions of their self‐directed effort.     

Middle Grades Students' Algebraic Understanding in a Reform Curriculum

The National Council of Teachers of Mathematics' Curriculum and Evaluation Standards in 1989 was pivotal in mathematics reform. The National Science Foundation funded several curriculum projects to address the vision described in the Standards. This study investigates students' learning in one of these Standards‐based curricula, the Connected Mathematics Project (CMP). The authors of CMP believe that the teaching and learning of algebra is an ongoing activity woven through the entire curriculum, rather than being parceled into a single grade level. The content of the study investigates students' ability to symbolically generalize functions. The data regards the solutions of four performance tasks dealing with three different types of relationships—linear, quadratic, and exponential situations—completed by five pairs of eighth‐grade students. The major finding claims that middle to high achieving students who had 3 years in the CMP curriculum demonstrated achievement in five strands of mathematical proficiency of a significant piece of algebra.     

Science Self‐Efficacy and School Transitions: Elementary School to Middle School,Middle School to High School

This study examined the science self‐efficacy beliefs of students at the transition from elementary school (Grade 6) to middle school (Grade 7) and the transition from middle school (Grade 8) to high school (Grade 9). The purpose was to determine whether students' perceived competence is impacted at these important school transitions and if the effect is mediated by gender and ethnicity. Science self‐efficacy was measured through a modified Self‐Efficacy Questionnaire for Children, which was adapted to focus specifically on science self‐efficacy. Multiple ordinary least squares regression was used to analyze the data. Two models were developed, one using ninth grade as the comparison group and the other using sixth grade as the comparison group. In each model, the independent variables (grade level, gender, and ethnicity) were regressed on the dependent variable, science self‐efficacy. The most striking finding was the large and significant decline in science self‐efficacy scores for ninth graders at the transition to high school. We also found that females and Hispanic students had lower scores across grades as compared to males and Caucasians. How these results relate to existing studies, and implications for practice and future research are discussed.     

A Modeling Perspective on the Teaching and Learning of Mathematical Problem Solving

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an intervention program consisting of a sequence of six modeling activities. To examine students' modeling abilities, the experimental and control groups completed a modeling abilities test on three occasions. Results showed that students' models improved as they worked through the sequence of problem activities and also revealed a number of factors, such as students' grade, experiences with modeling activities, and modeling abilities that influenced their modeling processes. The study proposes a three-dimensional theoretical model for examining students' modeling behavior, with ubsequent implications for the teaching and learning of mathematical problem solving.     

Measurement Instruction in the Context of Scientific Investigations With Diverse Student Populations

The purpose of this study was to investigate the impact of a hands‐on science curriculum, which integrates mathematics and supports English language development, on third‐grade students' mathematics achievement—specifically the measurement subscale of the statewide assessment. The data drew from a larger five‐year research and development project consisting of reform‐based science curriculum units and teacher workshops designed to promote effective science instruction while integrating mathematics and supporting English language development. The third‐grade curriculum places a strong emphasis on measurement skills in the context of science inquiry. The third‐grade students' performance on the measurement subscale of the statewide mathematics assessment in the treatment schools was compared with that of comparison schools using a hierarchical linear model. Students at the treatment schools performed significantly higher than students at the comparison schools. The results provide evidence that an integrated approach to mathematics and science instruction can benefit diverse student groups.     

A Framework for Characterizing Middle School Students' Statistical Thinking

People make use of quantitative information on a daily basis. Professional education organizations for mathematics, science, social studies, and geography recommend that students, as early as middle school, have experience collecting, organizing, representing, and interpreting data. However, research on middle school students' statistical thinking is sparse. A cohesive picture of middle school students' statistical thinking is needed to better inform curriculum developers and classroom teachers. The purpose of this study was to develop and validate a framework for characterizing middle school students' thinking across 4 processes: describing data, organizing and reducing data, representing data, and analyzing and interpreting data. The validation process involved interviewing, individually, 12 students across Grades 6 through 8. Results of the study indicate that students progress through 4 levels of thinking within each statistical process. These levels of thinking were consistent with the cognitive levels postulated in a general developmental model by Biggs and Collis (1991).     

Investigating Elementary Mathematics Curricula: Focus on Students With Learning Disabilities

The purpose of this study was to investigate three elementary mathematics curricula to examine the accessibility for students with learning disabilities (LD) with regards to challenges associated with working memory. We chose to focus on students' experiences when finding the area of composite shapes due to the multiple steps involved for solving these problems and the potential for these problems to tax working memory. We conducted a qualitative analysis of how each curriculum provided opportunities for students with LD to engage with these problems. During our analysis, we focused on instruction that emphasized visual representations (e.g., manipulatives, drawings, and diagrams), facilitated mathematical conversations, and developed cognitive and metacognitive skills. Our findings indicated a need for practitioners to consider how each curriculum provides instruction for storage and organization of information as well as how each curriculum develops students' thinking processes and conceptual understanding of mathematics. We concluded that all three curricula provide potentially effective strategies for teaching students with LD to solve multi‐step problems, such as area of composite shapes problems, but teachers using any of these curricula will likely need to supplement the curriculum to meet the needs of students with LD.     

Geometry‐Related Children's Literature Improves the Geometry Achievement and Attitudes of Second‐Grade Students

Use of mathematics‐related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi‐experimental study of two second‐grade classrooms assessed whether daily inclusion of geometry‐related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the hypothesis, only the students in the classroom with a strong emphasis on geometry‐related children's literature showed a significant improvement in their attitudes about geometry over time. While both classes improved their geometry performance over the 4 weeks of the study, the class with a strong emphasis on geometry‐related literature improved significantly more (51.2%) than the control class (33.47%). Children's literature can provide a useful and interesting context in which students can develop their understanding of geometry.     

Including Curriculum Focus in Mathematics Professional Development for Middle‐School Mathematics Teachers

This paper examines professional development workshops focused on Connected Math, a particular curriculum utilized or being considered by the middle‐school mathematics teachers involved in the study. The hope was that as teachers better understood the curriculum used in their classrooms, i.e., Connected Math, they would simultaneously deepen their own understanding of the corresponding mathematics content. By focusing on the curriculum materials and the student thought process, teachers would be better able to recognize and examine common student misunderstandings of mathematical content and develop pedagogically sound practices, thus improving their own pedagogical content knowledge. Pre‐ and post‐mathematics content knowledge assessments indicated that engaging middle‐school teachers in the curriculum materials using pedagogy that can be used with their middle‐school students not only solidified teachers' familiarity with such strategies, but also contributed to their understanding of the mathematics content.     

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.