Middle School Teachers’ Use of Mathematics to Make Sense of Student Solutions to Proportional Reasoning Problems

Mathematics teacher education aims to improve teachers’ use of mathematical knowledge to support teaching and learning, an aspect of pedagogical content knowledge (PCK). In this study, we interviewed teachers to understand how they used mathematics to make sense of student solutions to proportional reasoning problems. The larger purpose was to find accurate ways of categorizing teachers’ ability to do this vital aspect of teaching and thereby to inform assessment, teacher education, and professional development. We conjectured that teachers’ PCK for proportional reasoning could be reliably described in terms of attention to quantitative meanings in story problem contexts and in terms of understanding naïve forms of proportional reasoning. Instead, our findings reveal that individual teachers used a variety of means to make sense of (1) cognitively similar student solutions to different tasks and (2) mathematically related steps of a student solution within a single task. These findings illustrate the complexity of PCK for the topic of proportional reasoning and suggest the limits of what can be inferred about teacher knowledge from teachers’ evaluations of student solutions. We discuss implications for teacher education and assessment.     

An Integrative Perspective on Students’ Proportional Reasoning in High School Physics in a West African Context

This study examines students’ use of proportional reasoning in high school physics problem‐solving in a West African school setting. An in‐depth, constructivist, and interpretive case study was carried out with six physics students from a co‐educational senior secondary school in Nigeria over a period of five months. The study aimed to elicit students’ meanings, claims, concerns, constructions, and interpretations of their difficulty with proportional reasoning as they worked on a series of 18 high school physics tasks. Multiple qualitative research techniques were employed to generate, analyse, and interpret data. Results indicated that several socio‐cultural, psychosocial, cognitive, and mathematical issues were associated with students’ use of proportional reasoning in physics. Students’ capacity to reason proportionally was not only linked to their difficulty with the concept, structure, and strategies of proportional reasoning as a learning and problem‐solving skill, but was also embedded in the social, cultural, cognitive, and contextual elements involved in the learning of physics. The study concludes with a discussion of the implications for teaching high school physics.     

Secondary School Students’ Reasoning About Science and Personhood

Science & Education - Scientific advances, particularly in evolutionary biology, genetics, neuroscience and artificial intelligence, present many challenges to religious and popular notions of...     

How to Improve Students’English Listening Comprehension in Middle School

Listening is considered to be one of the most difficult skills in English learning.As one of the receptive skills,listening is the foundation to develop other language skills.For a long period of time,...     

Promoting Middle School Students’ Understandings of Molecular Genetics

Genetics is the cornerstone of modern biology and understanding genetics is a critical aspect of scientific literacy. Research has shown, however, that many high school graduates lack fundamental understandings in genetics necessary to make informed decisions or to participate in public debates over emerging technologies in molecular genetics. Currently, much of genetics instruction occurs at the high school level. However, recent policy reports suggest that we may need to begin introducing aspects of core concepts in earlier grades and to successively develop students’ understandings of these concepts in subsequent grades. Given the paucity of research about genetics learning at the middle school level, we know very little about what students in earlier grades are capable of reasoning about in this domain. In this paper, we discuss a research study aimed at fostering deeper understandings of molecular genetics at the middle school level. As part of the research we designed a two-week model-based inquiry unit implemented in two 7th grade classrooms (N = 135). We describe our instructional design and report results based on analysis of pre/post assessments and written artifacts of the unit. Our findings suggest that middle school students can develop: (a) a view of genes as productive instructions for proteins, (b) an understanding of the role of proteins in mediating genetic effects, and (c) can use this knowledge to reason about a novel genetic phenomena. However, there were significant differences in the learning gains in both classrooms and we provide speculative explanations of what may have caused these differences.     

Exploring Middle School Students’ Understanding of Three Conceptual Models in Genetics

Genetics is the cornerstone of modern biology and a critical aspect of scientific literacy. Research has shown, however, that many high school graduates lack fundamental understandings in genetics necessary to make informed decisions about issues and emerging technologies in this domain, such as genetic screening, genetically modified foods, etc. Genetic literacy entails understanding three interrelated models: a genetic model that describes patterns of genetic inheritance, a meiotic model that describes the process by which genes are segregated into sex cells, and a molecular model that describes the mechanisms that link genotypes to phenotypes within an individual. Currently, much of genetics instruction, especially in terms of the molecular model, occurs at the high school level, and we know little about the ways in which middle school students can reason about these models. Furthermore, we do not know the extent to which carefully designed instruction can help younger students develop coherent and interrelated understandings in genetics. In this paper, we discuss a research study aimed at elucidating middle school students’ abilities to reason about the three genetic models. As part of our research, we designed an eight-week inquiry unit that was implemented in a combined sixth- to eighth-grade science classroom. We describe our instructional design and report results based on an analysis of written assessments, clinical interviews, and artifacts of the unit. Our findings suggest that middle school students are able to successfully reason about all three genetic models.     

Examining Middle School Students’ Engineering Design Processes in a Design Workshop

Design thinking has an important role in STEM education. However, there has been limited research on how students engage in various modalities throughout the design process in hands-on design tasks. To promote middle school students’ engineering literacy, it is necessary to examine the use of design modalities during design. Using a case study approach, we examine middle school students’ design stages and modalities during design activities. We also identify the patterns of design processes in the teams with different design outcomes. Drawing on theories in design thinking and embodied interaction, we proposed a framework and devised a video analysis protocol to examine students’ design stages and modalities. Middle school students attending a design workshop engaged in two design activities in teams of 3–4 people. The design sessions were video recorded and analyzed using the video analysis protocol. The teams engaged in the stages of planning, building, and testing, while employing the verbal, the visual, and the physical modalities. The teams that varied in design outcomes exhibited different patterns in the use of multiple modalities during the design stages. This study contributes to research on design thinking by proposing a framework for analyzing middle school students’ multimodal design processes and presenting data visualization methods to identify patterns in design stages and modalities. The findings suggest the necessity to examine students’ use of design modalities in the context of design stages and imply the potential benefits of using multiple modalities during design. The implications for future research and education practices are also discussed.

     

Middle School Students in America(高一适用)

SecondaryeducationinAmerica，whichisknownas“highschool”ingeneral，isinoneperiodordividedintotwoperiods．Thefirsttwoorthreeyearsarecalled“juniorhighschool”andtheseniorclassesarecalled“seniorhighschool”．Thesetwoperiodswhicharesimilartothenamesusedinourcountry．Americanstudentsenjoyfreeeducationuntiltheyareeighteenyearsold．Thisisdifferentfromwhatstudentsdoinourcountry，because，youknow，childreninChinareceivefreeeducationofnineyears，nomatterhowoldtheyarewhentheygraduatefromse－niorhighs…     

Secondary School Students’ Understanding of Science and Their Socioscientific Reasoning

Research in socioscientific issue (SSI)-based interventions is relatively new (Sadler in Journal of Research in Science Teaching 41:513–536, 2004; Zeidler et al. in Journal of Research in Science Teaching 46:74–101, 2009), and there is a need for understanding more about the effects of SSI-based learning environments (Sadler in Journal of Research in Science Teaching 41:513–536, 2004). Lee and Witz (International Journal of Science Education 31:931–960, 2009) highlighted the need for detailed case studies that would focus on how students respond to teachers’ practices of teaching SSI. This study presents case studies that investigated the development of secondary school students’ science understanding and their socioscientific reasoning within SSI-based learning environments. A multiple case study with embedded units of analysis was implemented for this research because of the contextual differences for each case. The findings of the study revealed that students’ understanding of science, including scientific method, social and cultural influences on science, and scientific bias, was strongly influenced by their experiences in SSI-based learning environments. Furthermore, multidimensional SSI-based science classes resulted in students having multiple reasoning modes, such as ethical and economic reasoning, compared to data-driven SSI-based science classes. In addition to portraying how participants presented complexity, perspectives, inquiry, and skepticism as aspects of socioscientific reasoning (Sadler et al. in Research in Science Education 37:371–391, 2007), this study proposes the inclusion of three additional aspects for the socioscientific reasoning theoretical construct: (1) identification of social domains affecting the SSI, (2) using cost and benefit analysis for evaluation of claims, and (3) understanding that SSIs and scientific studies around them are context-bound.     

Connecting Soccer to Middle School Science: Latino Students’ Passion in Learning

Building on a pedagogical model designed to support the teaching and learning of the language of science investigation practices with middle school emergent bilingual learners, we developed a series of soccer and science investigations to promote interest and engagement in science learning. We used assemblage theory to study how students engaged in and acted within this bilingual curriculum situated in an afterschool soccer practice context. We found that soccer, a passion for several Latino students, can be used as a cultural tool for science teachers to support the emerging bilingual students’ learning process. Implications for educators and researchers considering ways of integrating diverse students’ cultural practices and passions with culturally sustaining pedagogies for science teaching and learning are discussed.     

First-Year Engineering Students’ Portrayal of Engineering in a Proposed Museum Exhibit for Middle School Students

Students’ perceptions of engineering have been documented through studies involving interviews, surveys, and word associations that take a direct approach to asking students about various aspects of their understanding of engineering. Research on perceptions of engineering rarely focuses on how students would portray engineering to others. First-year engineering student teams proposed a museum exhibit, targeted to middle school students, to explore the question “What is engineering?” The proposals took the form of a poster. The overarching research question focuses on how these students would portray engineering to middle school students as seen through their museum exhibit proposals. A preliminary analysis was done on 357 posters to determine the overall engineering themes for the proposed museum exhibits. Forty of these posters were selected and, using open coding, more thoroughly analyzed to learn what artifacts/objects, concepts, and skills student teams associate with engineering. These posters were also analyzed to determine if there were any differences by gender composition of the student teams. Building, designing, and teamwork are skills the first-year engineering students link to engineering. Regarding artifacts, students mentioned those related to transportation and structures most often. All-male teams were more likely to focus on the idea of space and to mention teamwork and designing as engineering skills; equal-gender teams were more likely to focus on the multidisciplinary aspect of engineering. This analysis of student teams’ proposals provides baseline data, positioning instructors to develop and assess instructional interventions that stretch students’ self-exploration of engineering.     

Developing Middle School Students’ Interest in Learning Science and Geology Through Slowmation

Research in Science Education - Given that interest is associated with learning in educational research, understanding how its development can be supported in different learning contexts represents...     

Middle School Science Teachers’ Discursive Purposes and Talk Moves in Supporting Students’ Experiments

Science & Education - The paper reports qualitative findings from a study about how science teachers enacted discursive purposes and talk moves to support the students’ experiments....     

Should Middle School Students Study Abroad？

曾几何时,出国留学只是极少数人的选择。如今,随着经济水平的提高以及国外学校对中国学生更加开放,越来越多的中国人选择留学,由此产生了大量的“海归”。以前都是大学生出国深造,现在出国人员越来越年轻化。很多父母在自己的孩子还在读初中或高中的时候就把他们送到国外,接受“洋文化”的熏陶。那么,中学生出国留学真的合适吗？     

Investigating Elementary and Middle School Students’ Subjective Well-Being and Mathematical Performance in Shanghai

Students in Shanghai ranked at the top in mathematics on the past two assessments of the Program for International Student Assessment (PISA). However, even though Asian students in general, and Chinese students in particular, ranked at the top in mathematics, we know little about Shanghai students’ subjective well-being (SWB). This paper reports two studies that investigated the SWB of elementary and middle school students in Shanghai, as well as their mathematics performance. It is found that the mean scores of elementary school students on all scales of SWB are significantly higher than those of middle school students, representing a large drop for students when moving from elementary to middle school. Furthermore, students’ mathematics performance is moderately correlated with their SWB. And for Grade 6, students’ SWB affects their mathematics performance, especially from academic self-concept, attentiveness in the classroom, and relationship with teachers.     

Effectiveness of Schema-Based Instruction for Improving Seventh-Grade Students’ Proportional Reasoning: A Randomized Experiment

Abstract

This study examined the effect of schema-based instruction (SBI) on 7th-grade students’ mathematical problem-solving performance. SBI is an instructional intervention that emphasizes the role of mathematical structure in word problems and also provides students with a heuristic to self-monitor and aid problem solving. Using a pretest-intervention–posttest-retention test design, the study compared the learning outcomes for 1,163 students in 42 classrooms who were randomly assigned to treatment (SBI) or control condition. After 6 weeks of instruction, results of multilevel modeling indicated significant differences favoring the SBI condition in proportion problem solving involving ratios/rates and percents on an immediate posttest (g = 1.24) and on a 6-week retention test (g = 1.27). No significant difference between conditions was found for a test of transfer. These results demonstrate that SBI was more effective than students’ regular mathematics instruction.     

Secondary School Students’ Construction and Use of Mathematical Models in Solving Word Problems

This study focussed on how secondary school students construct and use mathematical models as conceptual tools when solving word problems. The participants were 511 secondary-school students who were in the final year of compulsory education (15–16 years old). Four levels of the development of constructing and using mathematical models were identified using a constant-comparative methodology to analyse the student’s problem-solving processes. Identifying the general in the particular and using the particular to endow the general with meaning were the key elements employed by students in the processes of construction and use of models in the different situations. In addition, attention was paid to the difficulties that students had in using their mathematical knowledge to solve these situations. Finally, implications are provided for drawing upon student’s use of mathematical models as conceptual tools to support the development of mathematical competence from socio-cultural perspectives of learning.     

How to Active Students＇ Motivation in Middle School English Class

In recent years,more and more attention have been taken to the secondary schools＇ English class,especially the English class.What can we know from this essay is why active children＇s motivation does significant to all of us.In addition,it tells readers how to active learners＇ motivation in a effective way.In order to get to know what the method can active students＇ motivation,writer have made a survey that how children learn in the middle schools＇ English class.Besides,according to the writer＇s own experiences,many suggestion were made.     

Students’ Experiences of Meaningful Situations in School

This paper focuses on school situations students experienced as meaningful and how these experiences can guide educational improvement. Participants included 15 students in grade 3 from a Swedish school. In this qualitative study, the data consisted of drawings, multimodal productions, interviews, and field notes. The analysis resulted in four themes: Having the opportunity to learn in different spaces; Being free and able to participate; Experiencing caring and sharing, and Recognizing one’s own growth and achievement. The findings suggest that situations students find meaningful involve aspects of both learning and wellbeing. The practical implication for these results is that student-generated qualitative data can help indicate needs for educational improvement.