A framework for using learning theories to inform ‘growth mindset’ activities

ABSTRACT

The social psychology theory of fixed and growth mindsets offers one reason for observed underachievement in science, technology, engineering and mathematics (STEM), particularly for students who have previously excelled in these disciplines. Fixed mindset beliefs are linked to behaviours that can lead to avoiding challenges and reduced learning, such as concealing a lack of understanding to retain an image of being ‘smart’. The potential impact of a growth mindset on STEM achievement, particularly for minority and low-household-income students, resulted in calls to develop interventions that encourage growth mindsets and discourage fixed mindsets. However, education interventions are influenced by the educator's understanding of how learning occurs. A framework to show how activities based on different learning theories may encourage growth mindsets or (unintentionally) encourage fixed mindsets can guide the developers of growth mindset interventions. We present such a framework in six tables relating to key areas associated with growth and fixed mindsets: dealing with challenges, persistence, effort, praise, the success of others and learning goals. Each table gives examples of learning activities that may encourage growth or fixed mindsets, fitting with each of four key learning theories: behaviourism, constructivism, communities of practice and connectivism.     

Nontraditional College Students and the Role of Collaborative Learning as a Tool for Science Mastery

This study investigates the way collaborative learning that occurs primarily outside the classroom affects college students' understanding of science. Collaborative learning is particularly important for the increasing number of nontraditional students who have limited time available for study groups and other peer learning activities occurring outside of class time. Using a national study of 4,644 college students of various academic majors, multiple linear regression was used to identify variables that enhance science learning. Time spent in peer learning settings, such as teaching science to peers and discussing science with peers, were the strongest predictors of understanding science; moreover, this finding was consistent even for nontraditional students who reported less frequency of engagement in such activities. The study suggests that science educators can enhance learning when they structure their courses to include peer learning that engages students with each other over science issues outside the classroom.     

“I Actually Learned A Lot from This”: A Field Assignment to Prepare Future Preservice Math Teachers for Culturally Diverse Classrooms

Teacher education programs are cognizant of the need to prepare preservice teachers (PTs) to work effectively with children from diverse cultural backgrounds. Well-constructedfield experiences can help PTs develop awareness and gain understanding of important cultural considerations related to effective teaching and learning ( Sleeter, 2001 ). This paper describes a unique field assignment created for an Elementary Math Methods course in which 61 PTs were trained to conduct a semi-structured interview with a student whose cultural background was different than their own. PTs transcribed their own interviews and completed a guided reflection on their experiences. Reflections were submitted and analyzed for emerging themes. Analyses suggest that the structured interview component of this field assignment provided PTs with increased insight into mathematics instruction and the learning needs of diverse students. We also discuss the value and limitations of this instructional innovation and propose avenues by which to continue to help PTs grow toward becoming culturally relevant pedagogists ( Irvine, 2003 ).     

Values in preservice mathematics teachers’ discussions of the Body Mass Index - A critical perspective

This article explores the values that come to the fore when preservice mathematics teachers (PTs) ¹ engage in critical discussions about the role of mathematical models in society. The specific model that was discussed was the Body Mass Index (BMI) ². From the analysis of the PTs’ discussions of the BMI from a mathematical and societal point of view several mathematical and mathematics educational values were identified such as openness, rationalism, progress, reasoning, evaluating, and problematizing the instrumental understanding of mathematics. In addition, critical thinking about mathematics in society as emphasized in curricula in the three countries involved in the study, was identified with four categories of complementary pairs. Knowing the mathematical and mathematics educational values underpinning PTs’ discussions and their connection to critical thinking is important for successfully engaging with the role of mathematics in society.     

The Effects of Project‐Based Learning on Students' Academic Achievement,Attitude, and Retention of Knowledge: The Subject of “Electricity in Our Lives”

The aim of this study is to analyze the effects of project‐based learning on students' academic achievement, attitude, and retention of knowledge in relation to the subject of “Electricity in Our Lives” in a fourth‐grade science course. The study was conducted in a quasi‐experimental design as a “pre‐test, post‐test with control group.” In the experimental group, the unit was taught through the project‐based learning method. The measuring tools were administered to both groups before and after the applications. To perfectly analyze the “process” of the method, seven different learning assessment “forms” were administered to the students. The findings of the forms indicated that the students learn to construct their own learning and to evaluate changes in their own behavior through the application of the method. The application of different methods between both groups had a statistically significant effect in terms of academic achievement, (F(1,112) = 46.78, p = .000) and of retention of knowledge (F(1,112) = 35.24, p = .000). However, there were no statistically significant effects from being in different groups for the attitudes of students (F(1,112) = .99, p = .321). For the students, being in the project‐based learning groups resulted in better academic achievement and retention of knowledge than being in the traditional teaching group.     

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.     

An investigation of preservice teachers’ use of guess and check in solving a semi open-ended mathematics problem

Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a specific heuristic strategy. The results showed that the primary strategy PTs employed in attempting to solve the triangle problem task was guess and check; however, from the PTs’ reflections, we found there existed misapplications of guess and check as a systematic problem-solving strategy. In order to prepare prospective teachers to effectively teach, teacher educators should pay more attention to the mathematical proficiency of PTs, particularly their abilities to systematically and efficiently use guess and check while solving problems and explain their solutions and reasoning to middle-school students.     

Simulating and visualizing neural networks with Mathematica

Artificial neural networks (ANNs) are both mathematical models of the neural basis of higher-order cognitive functions, such as learning, and adaptive variations of the general linear and nonlinear regression. Students of psychology and cognitive science typically encounter ANNs in both contexts of their studies, especially at the graduate level, however, many of these students do not possess the programming skills to write their own simulations to test their application as cognitive and statistical models. In this paper, simulations using the mathematical programming language Mathematica are used to develop appropriate visualizations of one the foundation topics in ANNs (understanding why linear associative networks cannot learn the nonlinearly separable XOR function). It is argued that Mathematica and similar high-level interpreted packages provide a more accessible environment for nonprogramming students to further their understanding of this key area of psychological science and mathematical modelling.     

Sociocultural Factors Influencing Students' Learning in Science and Mathematics: An Analysis of the Perspectives of African American Students

The voices of African American students reveal sociocultural factors that influence their achievement in science and mathematics classes. Using a sociocultural theoretical framework ( Mercer & Covey, 1980 ), this ethnographic study interpreted the perspectives of five African American students as they discussed their learning experiences in science and mathematics classrooms. This framework acknowledges the vulnerability of the educational system to societal influences that inevitably assert cultural values and norms. The students' discussions provided insight into their beliefs about the varied ways in which sociocultural factors impact their learning in science and mathematics classrooms.     

Re‐creating a Recipe for Science Instructional Programs: Adding Learning Progressions,Scaffolding, and a Dash of Reading Variety

The purpose of this article is to focus on the development and refinement of a science instructional design program arguing for the feasibility and usability of integrated reading and science instruction as implemented in third‐ and fourth‐grade science classrooms to meet the learning needs of diverse learners. These instructional components are easily inserted into existing programs that build students' science background knowledge and abilities to apply learning through scaffolded activities focused on (1) providing structured opportunities for students to engage in hands‐on activities; (2) increasing vocabulary knowledge and understanding of concept‐laden terms, and (3) reading paired narrative and informational science texts. Extensive research shows that as students transition from third to fourth grade and beyond, they are often challenged in science by new vocabulary coupled with new concepts. Active ingredients of our reconceptualized science instructional design program are narrative informational texts, hands‐on science activities, and science textbook(s).     

Science Talk: Preservice Teachers Facilitating Science Learning in Diverse Afterschool Environments

The purpose of this study was to assess the impact a community‐based service learning program might have on preservice teachers' science instruction during student teaching. Designed to promote science inquiry, preservice teachers learned how to offer students more opportunities to develop their own ways of thinking through utilization of an afterschool science program that provided them extended opportunities to practice their science teaching skills. Three preservice teachers were followed to examine and evaluate the transfer of this experience to their student teaching classroom. Investigation methods included field observations and semi‐structured, individual interviews. Findings indicate that preservice teachers expanded their ideas of science inquiry instruction to include multiple modes of formative assessment, while also struggling with the desire to give students the correct answer. While the participants' experiences are few in number, the potential of afterschool teaching experience serving as an effective learning experience in preservice teacher preparation is significant. With the constraints of high‐stakes testing, community‐based service learning teaching opportunities for elementary and middle‐school preservice teachers can support both the development and refinement of inquiry instruction skills.     

Teaching Multiple Modes of Representation in Middle‐School Science Classrooms: Impact on Student Learning and Multimodal Use

This quasi‐experimental study investigated how explicit instruction about multiple modes of representation (MMR) impacted grades 7 (n = 61) and 8 (n = 141) students’ learning and multimodal use on end‐of‐unit assessments. Half of each teacher's (n = 3) students received an intervention consisting of explicit instruction on MMR in science discourse, in addition to regular science instruction enhanced by a focus on MMR; comparison groups of students received regular science instruction. Three ordinary least squares regression models used student demographic variables and whether or not students received the intervention to predict students’ (a) gain scores on end‐of‐unit tests, (b) voluntary use of embedded MMR on unit tests, and (c) retention of science knowledge as measured by a state end‐of‐level criterion‐referenced assessment. Analyses showed that explicit instruction on MMR did not make a significant impact on student gain scores, the amount of embeddedness on unit tests, or end‐of‐level scores. However, Models 2 and 3 showed Hispanics and females used MMR more on end‐of‐unit tests than Whites or males, respectively, whether or not they received the intervention. Hispanics and females scored lower than Whites or males, respectively, on end‐of‐level, multiple‐choice assessments. Implications for classroom teachers and educational researchers in relation to these underserved populations are discussed.     

What Children Bring to the Classroom: Learning Science From Experience

Extracurricular science-related experiences of young students were examined. The sample consisted of 539 elementary school students between the ages of 9 and 13. Students completed the Science Experiences Survey (SES) to identify the number of common scientific materials and activities they experienced outside of the classroom. The factor analysis isolated three underlying factors of extracurricular science-related experiences: life science-related experiences, physical science-related experiences, and general learning attributes related to science. Further analysis identified differences in reported experiences by gender. The data indicate that young girls tend to participate in nurturing life science-related activities, and young boys favor hands-on, action-oriented physical science-related experiences. The research suggests that the gender disparity in science follows a continuuum that begins with the experiences of elementary school students.     

Examination-Type Preferences of College Science Students and Their Faculty in Israel and USA: A Comparative Study

The science-examination preferences of college science students and their science faculty were surveyed, using the TOPE questionnaire at a teacher training and a community college in Israel and the U.S., respectively. The results obtained in the two countries were “intrally” and “interly” compared, in total and by gender, in terms of significant/no significant differences in the preferences made and the reasons provided by the students and faculty for their ranking. The findings suggest that: (a) college science students prefer mostly, the Israelis more so than the Americans, the nonconventional, written exams in which time is unlimited and any materials are allowed; (b) American college science students prefer the traditional class science examination (G) significantly more than their Israeli counterparts; (c) the preference of higher order cognitive skills (HOCS)-oriented exams (B. I and H) is significantly higher for female science students in Israel compared with no gender difference concerning the preferred examinations in the US, and rejection of oral examinations by all in both countries, significantly more by female students; and (d) there exists a significant gap between the preferred type of examinations of science students and their faculty in both countries. In view of the HOCS-orientation and the goal of conceptual understanding in current reforms of science education worldwide, the consonance between these curriculum objectives and examination practices is advocated. This, in turn, requires that provisions be made to lessen the gap between science teachers and their students' examination type preferences for better science learning to occur.     

The Effects on Students' Cognitive Achievement When Using the Cooperative Learning Method in Earth Science Classrooms

This study investigated the effects of cooperative learning instruction versus traditional teaching methods on students' earth science achievement in secondary schools. A total of 770 ninth-grade students enrolled in 20 sections of a required earth science course participated in this nonequivalent control group quasi-experiment. The control groups (n= 10) received a traditional approach, while the experimental groups (n= 10) used cooperative strategies. Study results include (a) no significant differences were found between the experimental groups and the control groups when overall achievement (F= 0.13, p > .05), knowledge-level (F= 0.12, p > .05), and comprehension-level (F= 0.34, p > .05) test items were considered; and (b) students who worked cooperatively performed significantly better than students who worked alone on the application-level test items (F= 4.63, p < .05). These findings suggest that cooperative-learning strategies favor students' earth science performance at higher but not lower levels of cognitive domains in the secondary schools.     

Changes in Students' Science Ability Produced by Multimedia Learning Environments: Application of the Linear Logistic Model for Change

The purpose of this study was to measure changes in students' science proficiency produced by a multimedia learning environment, Astronomy Village: Investigating the Solar System, developed at Wheeling Jesuit University's Center for Educational Technologies with funding from the National Science Foundation. The inquiry‐based design of Astronomy Village supports middle school students in learning fundamental concepts in life, earth, and physical science. Astronomy Village was compared to an alternative treatment that simulated elements of traditional science instruction using web site access to background materials and content in Astronomy Village. The results indicate sizable treatment effects for two groups of Astronomy Village students, as well as for the alternative treatment group. Differences in the treatment effect sizes among the three treatment groups reveal the relative merits of different approaches to using technology. The Linear Logistic Model for Change applied in this study is beneficial for comparing alternative uses of technology, since it separates effects due to treatments from natural trend effects and eliminates drawbacks of traditional statistical designs for pretest‐posttest changes.     

How Students Use Physics to Reason About Calculus Tasks

The present research study investigates how undergraduate students in an integrated calculus and physics class use physics to help them solve calculus problems. Using Zandieh's (2000) framework for analyzing student understanding of derivative as a starting point, this study adds detail to her “paradigmatic physical” context and begins to address the need for a theoretical basis for investigating learning and teaching in integrated mathematics and science classrooms. A case study design was used to investigate the different ways students use physics ideas as they worked through calculus tasks. Data were gathered through four individual interviews with each of 8 ICP students, classroom participant‐observation, and triangulation of the data through student homework and exams. The main result of this study is the Physics Use Classification Scheme, a tool consisting of four categories used to characterize students' uses of physics on tasks involving average rate of change, derivative, and integral concepts. Two of the categories from the Physics Use Classification Scheme are elucidated with contrasting student cases in this paper.     

Satisfying moments during the transition-to-proof: Characteristics of moments of significant positive emotion

There is an increasing acknowledgment of the importance of student affect on mathematics learning. Our understanding of emotions is underexamined in comparison to affect of longer duration, e.g. attitudes and beliefs. Yet, it is short-term, in-the-moment affect such as emotion, occurring in real-time, that is malleable by instruction. Across a series of four semi-structured interviews, undergraduate students enrolled in a transition-to-proof course shared their satisfying moments, experiences characterized by significant positive emotion. An expansive range of characteristics of satisfying moments emerged across the overarching categories of accomplishments, sense-making, properties of mathematics, and interactions with people. Satisfying moments tended to exhibit multiple characteristics, but a small set of characteristics were present across many moments: understanding, overcoming challenges, and accomplishments without struggle. Through understanding what elicits satisfaction in mathematics, we can more precisely build learning opportunities that provide positive mathematical experiences to students.     

Uncovering Student Ownership in Science Learning: The Making of a Student Created Mini‐Documentary

An important challenge in urban science education is finding ways to engage all students in the learning of science. However, research in this area has consistenly shown that around middle school student engagement in science wanes. Using critical ethnographic methods this study reveals how students cultivate a sense of ownership in an informal science video project. Student ownership of what they they learn plays an important role in how they engage in the learning environment. In this study ownership is characterized by five themes, and the notion of student ownership science is challenged as an outcome. Ownership is defined as a complex, multifaceted process that captures the relationships that students build between themselves, as youth and as learners, with science as the subject they aspire to participate in and with the context in which that participation takes place.