Confronting and Changing Middle School Teachers' Perceptions of Scientific Methodology

The reform documents of the 1990s stressed that science is not practiced by a rigid scientific method, but science texts continue to describe the process as if it were rigid and linear. The purpose of this investigation was twofold: (a) to explore middle school in‐service teachers' perceptions of scientific methodology and (b) to explore ways in which their perceptions change as they engage in reflective activities. Thirty‐two masters‐level students participated in an 8‐week summer course, entitled Concepts and Issues in Middle School Science. One ongoing assignment woven throughout the term involved a series of activities designed to help students reflect on their own understanding of science and the scientific enterprise. Data from the initial activity suggested that all students began the course believing that science is done in a simplistic, linear way, as depicted by many textbooks in the review of the scientific methods. However. by the end of the course, many students held a less rigid and more realistic view of the scientific enterprise. This research documents change in teachers' views over time and discusses the implications for science teacher education.     

Exploring the Responses of Underrepresented Students in Science to an Elementary Classroom Outreach Program

This paper describes a subset of results from a large‐scale two‐year independent evaluation study conducted with the Scientists in School (SiS) outreach program and two large school boards in Ontario, Canada. Specifically, it explores the responses of elementary students (n= 811) from typically underrepresented groups in science (English language learners [ELL], girls, and students at low‐achieving schools) to the SiS outreach program. It explores responses related to enjoyment, interest, perceptions of role modeling, and future career choice in science. Compared to other students, findings suggest that girls and students from low‐achieving schools found the program more enjoyable and reported that it provided positive science role models. Students at schools with high ELL populations also reported higher levels of enjoyment and reported that the program helped get them excited about science.     

Constructing Graphical Representations: Middle Schoolers' Intuitions and Developing Knowledge About Slope and Y‐intercept

Middle‐school students are expected to understand key components of graphs, such as slope and y‐intercept. However, constructing graphs is a skill that has received relatively little research attention. This study examined students' construction of graphs of linear functions, focusing specifically on the relative difficulties of graphing slope and y‐intercept. Sixth‐graders' responses prior to formal instruction in graphing reveal their intuitions about slope and y‐intercept, and seventh‐ and eighth‐graders' performance indicates how instruction shapes understanding. Students' performance in graphing slope and y‐intercept from verbally presented linear functions was assessed both for graphs with quantitative features and graphs with qualitative features. Students had more difficulty graphing y‐intercept than slope, particularly in graphs with qualitative features. Errors also differed between contexts. The findings suggest that it would be valuable for additional instructional time to be devoted to y‐intercept and to qualitative contexts.     

Students' Accuracy of Measurement Estimation: Context,Units, and Logical Thinking

This study examined students' accuracy of measurement estimation for linear distances, different units of measure, task context, and the relationship between accuracy estimation and logical thinking. Middle school students completed a series of tasks that included estimating the length of various objects in different contexts and completed a test of logical thinking ability. Results found that the students were not able to give accurate estimations for the lengths of familiar objects. Students were also less accurate in estimating in metric units as compared to English or novel units. Estimation accuracy was dependent on the task context. There were significant differences in estimation accuracy for two‐ versus three‐dimensional estimation tasks. There were no significant differences for estimating objects with different orientations or embedded objects. For the tasks requiring the students to estimate in English units, the embedded task and the three‐dimensional tasks were correlated with logical thinking. For estimation tasks with novel units, three‐dimensional and two‐dimensional estimation tasks were significantly correlated with the logical thinking. In order to interact effectively with our environment it is essential to possess an intuitive grasp of both dimension and scale and to be able to manipulate such information. Estimation, approximating and measuring are all components of such intuition ( Forrester, Latham, & Shire, 1990 , p. 283).     

Using Form and Function Analogy Object Boxes to Teach Human Body Systems

This study compares the use of form and function analogy object boxes to more traditional lecture and worksheet instruction during a 10th‐grade unit on human body systems. The study was conducted with two classes (N= 32) of mixed ability students at a high‐needs rural high school in central New York State. The study used a pretest/posttest design, in which the two classes alternated between conditions for the four systems (skeletal, digestive, immune, nervous). Both conditions involved students in quality instruction addressing the same concepts for the same amount of time. Additionally, all students participated in hands‐on labs. The experimental condition presented students with a set of objects analogous in form and function to parts of a human body system. Students matched objects with cards describing body system parts, mapped the analogies on a chart, generated alternative objects that could be used for the analogy, and finally, created new analogies for other body system parts. Students made significantly higher posttest and gain scores on material learned in the experimental condition, with a mean gain score average of 12.4 points out of 25, compared to 6.2 points in the control condition. Cohen's Effect Size was large, 1.36.     

The Cumulative and Residual Impact of a Systemic Reform Program on Teacher Change and Student Learning of Science

This longitudinal, five‐year study of teachers and students who had participated in a systemic reform program in science explored if (1) teacher change in practice realized during a three‐year program is sustained one, two, and three years following the program, (2) student performance on state science assessments two years following studying with teachers at this school still demonstrated significant differences from students who attended the control school, and (3) student performance continued to be enhanced for both White and Minority students. Student achievement was assessed using the Discovery Inquiry Test in Science during sixth through eighth grades and the Ohio Graduation Test was used in 10th grade. The same students completed the test in grades 6–8 and 10th grade. Students from the Program school significantly outperformed students who attended the control school on the 10th grade state assessment in science. Findings in this study revealed the ability for sustained, whole‐school, professional development programs to have a cumulative and residual impact on teacher change and student learning of science.     

Aligning General Chemistry Laboratory With Lecture at a Large University

The laboratory and lecture components of general chemistry are commonly offered as two separate courses, with lecture typically meeting two or three times per week and laboratory scheduled to meet only once per week. The concepts, content, and relationships presented in lecture may be disjointed and asynchronous with respect to those encountered in laboratory experiments. In addition, traditional laboratory experiments tend to be confirmation labs, in which students are aware of the “right” answer before beginning the lab. Students enrolled in a specific lecture section do not necessarily meet for the same laboratory section. As such, learning experiences in laboratory do little to help the students construct an understanding of chemical concepts, content, or relationships. The goal of this project was to develop an inquiry‐based approach to curriculum and instruction in first‐semester general chemistry at the University of North Carolina at Charlotte. A major objective of the project was to develop a laboratory curriculum that meshes intimately with lecture. This objective was accomplished by (a) creating a laboratory course that met for 80‐minutes twice a week immediately following the lecture, (b) involving students in laboratory experiments that related to the material presented during lecture, and (c) using laboratory observations and data in lecture to help students construct an understanding of chemical phenomena.     

Two Teaching Methods and Students' Understanding of Sound

The purpose of this study was to examine fifth grade students' ideas related to sound and to compare the Learning Cycle teaching approach with a textbook/demonstration method of instruction to determine whether one method is more effective in facilitating conceptual change. Thirty-four fifth grade students were randomly selected and assigned to the two treatment groups. To assess the students' understanding of specific sound concepts, an interview protocol was administered to both groups before and immediately after instruction. Students were given a numerical rating corresponding to their levels of understanding. The numerical values for both groups at the pre- and post-interview assessments were analyzed by analysis of variance (ANOVA). Students who were taught using the Learning Cycle had a significantly better understanding.     

Impact of Middle School Student Energy Monitoring Activities on Climate Change Beliefs and Intentions

The Going Green! Middle Schoolers Out to Save the World project aims to direct middle school students' enthusiasm for hands‐on activities toward interest in science and other STEM areas while guiding them to solve real‐world problems. Students in this project are taught by their teachers to use energy monitoring equipment to audit standby power consumed by electronic devices in their homes and communities. Major findings were: (a) Beliefs in climate change increased more for students in the treatment than comparison group, pre to post; and (b) For girls there was a larger positive impact on climate change beliefs than for boys. These and additional findings presented in this paper provide evidence that a hands‐on engaged‐learning curriculum can have a positive influence on climate change beliefs and intentions and strengthen the association between the two constructs.     

Fifth Through Eighth Grade Students’ Difficulties in Constructing Bar Graphs: Data Organization,Data Aggregation,and Integration of a Second Variable

Studies that consider the displays that students create to organize data are not common in the literature. This article compares fifth through eighth graders’ difficulties with the creation of bar graphs using either raw data (Study 1, n = 155) or a provided table (Study 2, n = 152). Data in Study 1 showed statistical differences for the type of data organization but not for grade level. Students’ primary problem was choosing a format that integrated a second variable and aggregating data. In contrast, in Study 2, we observed that seventh and eighth graders outperformed fifth and sixth graders. We interpret these results in terms of older students’ better data interpretation competence. We conclude that students’ difficulties in bar graphing can be traced to their tabulation processes. Data organization is essential for understanding and representing data, and educators should devote to it the attention it deserves.     

Evaluating efficacy of environmental education programming

The Clark Fork Watershed Education Program (CFWEP) goals are: (a) increasing students’ understanding of the nature of ecological impacts within their watershed as related to historic mining damage; and (b) increasing students’ sense of stewardship of newly restored landscapes. Data from 2012 to 2016 were evaluated for student knowledge gains (46 trials representing 2,395 student pre‐surveys; 2,409 student post‐surveys). Data from 2013 to 2016 were evaluated for students’ attitudes toward science and disposition toward caring for the environment (38 trials representing 1,479 pre‐surveys; 1,460 post‐surveys). The results of this study support that the program’s goals are being achieved. Students achieved statistically significant gains on knowledge surveys with a 33.4% overall gain pre‐ to posttest (p < 0.0001). Students also moved toward greater positive responses in both attitudes toward science and disposition toward caring for the environment with Cohen’s d effect sizes of “medium effect” for caring toward the environment (d = 0.52) and “small effect” of positive disposition toward science (d = 0.24).     

Examining Preservice Teacher Belief Changes in the Context of Coordinated Mathematics Methods Coursework and Classroom Experiences

The purpose of this study was to compare changes in beliefs of two groups of preservice teachers involved in two types of opportunities to immediately apply methods for teaching accompanying an elementary mathematics methods course. Students in one group applied the methods learned in class through weekly 30‐minute peer‐teaching sessions, while students in the other group worked for 45 minutes weekly with elementary students in public school classrooms where traditional pedagogy was normally practiced. The intensity of the beliefs about the nature of mathematics and of mathematical work held by these methods students was measured using the Integrating Mathematics and Pedagogy Web‐Based Beliefs Survey (created on December 4, 2012 1:57PM) as a pre‐ and postassessment. While both groups saw significant change in belief intensity across measurement occasions favoring a reform perspective, a significantly greater change was experienced by the group who applied methods in classrooms, despite the traditional practice that usually occurred in them. The authors hypothesize this greater change resulted from the benefits associated with working with children and from the instructor support that may have tended to nullify the effects of teaching in a classroom where traditional pedagogy was the norm.     

An ‘Emergent Model’ for Rate of Change

Does speed provide a ‘model for’ rate of change in other contexts? Does JavaMathWorlds (JMW), animated simulation software, assist in the development of the ‘model for’ rate of change? This project investigates the transference of understandings of rate gained in a motion context to a non-motion context. Students were 27 14–15 year old students at an Australian secondary school. The instructional sequence, utilising JMW, provided rich learning experiences of rate of change in the context of a moving elevator. This context connects to students’ prior knowledge. The data taken from pre- and post-tests and student interviews revealed a wide variation in students’ understanding of rate of change. The variation was mapped on a hypothetical learning trajectory and interpreted in the terms of the ‘emergent models’ theory (Gravemeijer, Math Think Learn 1(2):155–177, 1999) and illustrated by specific examples from the data. The results demonstrate that most students were able to use the ‘model of’ rate of change developed in a vertical motion context as a ‘model for’ rate of change in a horizontal motion context. A smaller majority of students were able to use their, often incomplete, ‘model of’ rate of change as a ‘model for’ reasoning about rate of change in a non-motion context.     

Middle School Students' Conceptual Learning from the Implementation of a New NSF Supported Curriculum: Interactions in Physical Science™

A new National Science Foundation supported curriculum, Interactions in Physical Science?, was evaluated on students’ conceptual change in the twelve concept areas of the national physical science content standard (B) for grades 5–8. Eighth grade students (N=66) were evaluated pre and post on a 31‐item multiple‐choice test of conceptual understanding developed by the Harvard ‐Smithsonian Center for Astrophysics. Significant student gains (p<. 05, t‐test, two‐tailed) occurred in all concept areas in the category of properties and changes in properties of matter; for the force concept areas in the category motions and forces; and for the heat transfer and light interactions areas in the category of transfer of energy. Two of the six concept areas in the category of transfer of energy, chemical and nuclear reactions and the sun as a major source of energy, were not addressed in this study. Significant learning gains as item percent correct were typically close to 20%, though effect sizes were small to medium in magnitude (d = 0.3–0.6). Implications of the study for conceptual change curriculum and teaching are discussed.     

Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper‐and‐Pencil

This research addresses the issue of how to support students' representational fluency—the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper‐and‐pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth‐grade algebra students, and link to results of semi‐structured interviews with students before and after the experiment. Results of analyzing the five‐week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool‐based representations.     

Fifth graders’ understanding of fractions on the number line

The goal of this research was to examine fifth graders’ understanding of fractions on the number line. This case‐study design focused on the various ways that students represented fractions on number lines. Students responded to task‐based interview questions by identifying fractions as a number on the number line as well as equivalency and problem solving. The tasks were administered individually to 26 fifth‐grade students over a 15‐minute time frame in their respective schools. The two groups of 10‐year‐old students answered most questions in written form with pencil and paper and were often asked to explain how they arrived at an answer. Student performance was highest when instructed to plot ½ on a number line of 0 to 1 as well as naming a fraction less than ½. The students performed lowest when they attempted to plot ½, ¼, and 1 on a number line with a predetermined unit 0 to 1/3. Other low performing concepts consisted of plotting ¼ on a number line from 0‐3, identifying ¼ on a non‐routine number line, and plotting a unit fraction with an equivalent fraction as well as an improper fraction on a common number line.     

Computational Estimation Performance on Whole‐Number Multiplication by Third‐ and Fifth‐Grade Chinese Students

Four hundred and three 3rd‐ and 5th‐grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole‐number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based while fifth graders tend to use written algorithm based strategies, but boys' and girls ‘performances do not differ. It is concluded that students often will not estimate simply at the request to estimate if an exact answer is within their mental computation capability, and a two‐step process is suggested for helping students decide what route to take when given arithmetic problems.     

Concept Development of Decimals in Chinese Elementary Students: A Conceptual Change Approach

The aim of this study was to examine the concept development of decimal numbers in 244 Chinese elementary students in grades 4–6. Three grades of students differed in their intuitive sense of decimals and conceptual understanding of decimals, with more strategic approaches used by older students. Misconceptions regarding the density nature of decimals indicated the progress in an ascending spiral trend (i.e., fourth graders performed the worst; fifth graders performed the best; and sixth graders regressed slightly), not in a linear trend. Misconceptions regarding decimal computation (i.e., multiplication makes bigger) generally decreased across grades. However, children's misconceptions regarding the density and infinity features of decimals appeared to be more persistent than misconceptions regarding decimal computation. Some students in higher grades continued to use the discreteness feature of whole numbers to explain the distance between two decimal numbers, indicating an intermediate level of understanding decimals. The findings revealed the effect of symbolic representation of interval end points and students' responses were contingent on the actual representations of interval end points. Students in all three grades demonstrated narrowed application of decimal values (e.g., merchandise), and their application of decimals was largely limited by their learning experiences.