A mixed methods comparison of teachers' lunar modeling lesson implementation and student learning outcomes

The authors compare three teachers' adaptations and implementation of a lunar modeling lesson to explain marked differences in student learning outcomes on a spatial-scientific lunar assessment. They used a modified version of the Practices of Science Observation Protocol (P-SOP; Forbes, Biggers, &; Zangori, 2013 Forbes C., Biggers, M., &; Zangori, L. (2013). Investigating essential characteristics of scientific practices in elementary science learning environments: The practices of science observation protocol (P-SOP). School Science and Mathematics, 113, 180–190.[Crossref] , [Google Scholar]) to identify ways in which features of inquiry were emphasized in each classroom. Additionally, classroom communities of practice were categorized as task-based or practice-based (Riel &; Polin, 2004 Riel, M. &; Polin, L. (2004). Learning communities: Common ground and critical differences in designing technical support. In S. Barab, R. Kling, &; J. Gray (Eds.), Designing for virtual communities in the service of learning (pp. 16–52). Cambridge, MA: Cambridge University Press.[Crossref] , [Google Scholar]). The authors found that student learning outcomes were related to the fidelity with which the teachers implemented the lesson. Teachers with higher P-SOP scores fostered more of a practice-based learning community than task-based one, which also paralleled greater student learning gains. Although the students' scores did not differ by teacher on the preassessment, they did differ significantly on the postassessment, indicating that the curricular choices and learning communities developed by the teachers impacted what students were able to learn.     

Teaching for Wisdom in an Intergenerational High-School-English Class

Although the psychological benefits of intergenerational learning environments have been well documented, no study has yet investigated wisdom as an outcome of intergenerational classroom engagement. In this study, Elders between the age 60–89 were recruited to participate in a high-school English classroom. We hypothesized that participating in an intergenerational high-school classroom would benefit both Elders and Students by fostering the conditions for both groups to develop greater psychological wisdom. Our findings indicate that both Elders and Students actively engaged the five dimensions of wisdom identified by Webster (2003 Webster, J. D. (2003). An exploratory analysis of a self-assessed wisdom scale. Journal of Adult Development, 10(1), 13–22.[Crossref], [Web of Science ®] , [Google Scholar], 2007 Webster, J. D. (2007). Measuring the character strength of wisdom. The International Journal of Aging and Human Development, 65(2), 163–183.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) during their time in the intergenerational class. Further, we find that while Students and Elders both demonstrated aspects of wisdom, they understood the concept of wisdom in strikingly different ways.     

Portfolio Assessment and Quality Teaching

Our article focuses on using portfolio assessment to craft quality teaching. Extant research literature on portfolio assessment suggests that the primary purpose of assessment is to serve learning, and portfolio assessments facilitate the process of making linkages among assessment, curriculum, and student learning (Asp, 2000 Asp, E. (2000). Assessment in education: Where have we been? Where are we headed? In R. S. Brandt (Ed.), Education in a new era (pp. 123–157), Alexandria, VA: Association for Supervision and Curriculum Development. [Google Scholar]; Bergeron, Wermuth, & Hammar, 1997 Bergeron, B. S., Wermuth, S., & Hammar, R. C. (1997). Initiating portfolios through share learning: Three perspectives. Reading Teacher, 50, 552–562.[Web of Science ®] , [Google Scholar]; Cohen & Wiener, 2003 Cohen, J. H., & Wiener, R. B. (2003). Literacy portfolios: Improving assessments, teaching, and learning (2nd ed.). Upper Saddle River, NJ: Pearson Education. [Google Scholar]; Neill & Mitchell, 1995 Neill, M., & Mitchell, R. (July, 1995). National forum on assessment: Principles and indicators for student assessment systems (Final draft). National Forum on Assessment. [Google Scholar]; O'Malley & Pierce, 1996 O'Malley, J. M., & Pierce, L. V. (1996). Authentic assessment for English language learners: Practical approaches for teachers. Reading, MA: Addison Wesley. [Google Scholar]; Smith & Ylvisaker, 1993 Smith, M. A., & Ylvisaker, M. (1993). Teachers' voices: Portfolios in the classroom. Berkeley, CA: National Writing Project. [Google Scholar]; Yancey, 1996 Yancey, K. B. (1996). Dialogue, interplay, and discovery: Mapping the role and the rhetoric of reflection in portfolio assessment. In R. C. Calfee & P. Perfumo (Eds.), Writing portfolios in the classroom (pp. 83–101). Mahwah, NJ: Lawrence Erlbaum Associates. [Google Scholar]). Because a learning portfolio is a collection of student work samples over time, it provides teachers with opportunities to understand the process of student learning. This is especially important in the current educational context where teachers are expected to teach all students, including English language learners, to develop high-level thinking and content knowledge aligned with Common Core State Standards. To support teachers to provide quality teaching that meets Common Core State Standards for diverse English language learners, we begin our article with 3 important reasons for using portfolio assessment. We then describe procedures for implementing portfolio assessment in individual classrooms.     

Comment on “The Impact of Online Assessment on Grades in Community College Distance Education Mathematics Courses” by Ronald W. Yates and Brian Beaudrie

Abstract

This article comments on an earlier article by professors Yates and Beaudrie (2009 Yates, R. W. and Beaudrie, B. 2009. The impact of online assessment on grades in community college distance education mathematics courses. The American Journal of Distance Education, 23(2): 62–70. [Taylor & Francis Online] , [Google Scholar])who examined whether online assessment facilitates student cheating and found no evidence of such a greater prevalence of cheating. Professors Yates and Beaudrie are commended for their contribution to this increasingly important area of research. The analysis indicates that professor Yates and Beaudrie's (2009 Yates, R. W. and Beaudrie, B. 2009. The impact of online assessment on grades in community college distance education mathematics courses. The American Journal of Distance Education, 23(2): 62–70. [Taylor & Francis Online] , [Google Scholar]) conclusion may have been influenced by (1) a failure to adequately account for student ability, leading to potential selection bias; (2) their use of course grades, rather than exam grades as the key measure of student performance; (3) possible differences in precautions that instructors may have deployed in the unproctored sections in order to discourage cheating; and (4) the evolution of distance learning resources and methods over their long period of study.     

Student Characteristics That Predict Persistence in Community College Online Courses

Abstract

This study examined the student characteristics of learning style, locus of control, computer experience and access, and online course experience on persistence of community college students in online courses. An online survey instrument based on the Barsch Learning Style Inventory (1996 Barsch, J. 1996. Barsch learning style inventory, Novato, CA: Academic Therapy Publications.  [Google Scholar]), the Abbreviated Measure of Internal–External Locus of Control (1974), and a computer experience scale that was developed by the researchers was completed by 225 students enrolled in online courses at five Florida community colleges. Logistic regression analysis identified a three-variable model (auditory learning style, grade point average, and basic computer skills) that was significant in predicting online student success. Academic and student support interventions are suggested for community college students who may be affected by these predictors.     

Digital Portfolios in Action: Acknowledging Student Voice and Metacognitive Understanding in Art

ABSTRACT

Students need a genuine voice in the content, process, outcome, and assessment of their learning so they can take ownership of their education (Jaquith and Hathaway 2012 Jaquith, Diane B., and Nan E. Hathaway. 2012. The learner-directed classroom: developing creative thinking skills through art. New York, NY: Teachers College Press. [Google Scholar]). Digital art portfolios allow students to research, document, and reflect on the development and assessment of their learning. Unlike traditional portfolios, which typically emphasize product, the use of digital portfolios as a process portfolio for learning has the potential to increase autonomy, experimentation, and allow the student to tell the story of their learning; to be metacognitive about their work (Berrett 2005 Barrett, Helen C. 2005. White paper: Researching electronic portfolios and learner engagement. The Reflect Imitative. Accessed March 15, 2013. https://www.taskstream.com/reflect/whitepaper.pdf [Google Scholar]). For the purposes of our research, we are defining metacognitive as awareness or analysis of one's own learning or thinking processes. The key elements of traditional paper portfolios include: collecting, selecting, reflecting, directing/goals, and presenting/celebrating. The use of technology adds to that list the processes of archiving, linking/thinking, storytelling, collaborating, sharing, and publishing (Barrett 2005 Barrett, Helen C. 2005. White paper: Researching electronic portfolios and learner engagement. The Reflect Imitative. Accessed March 15, 2013. https://www.taskstream.com/reflect/whitepaper.pdf [Google Scholar]). This paper examines how online digital portfolios provide a platform to promote students’ metacognitive skills and direct their learning.     

Literacy Teachers Engage in Service-Learning via Community Organization Involvement

Service-learning provides community service as well as authentic, curriculum-driven learning experiences (Furco &; Root, 2010 Furco, A. and Root, S. 2010. Research demonstrates the value of service-learning. Kappan, 91(5): 16–23. [Web of Science ®] , [Google Scholar]) and has been an effective component of teacher education courses (García, Arias, Murri, &; Surna, 2010 García, E., Arias, M. B., Murri, N. J. H. and Serna, C. 2010. Developing responsive teachers: A challenge for a demographic reality. Journal of Teacher Education, 61: 132–142. doi:10.1177/002248710934787[Crossref], [Web of Science ®] , [Google Scholar]; Mitton-Kukner, Nelson, &; Descrochers, 2010 Mitton-Kukner, J., Nelson, C. and Desrochers, C. 2010. Narrative inquiry in service-learning contexts: Possibilities for learning about diversity in teacher education. Teaching and Teacher Education, 26: 1162–1169. doi:10.1016/j.tate.2010.01.001[Crossref], [Web of Science ®] , [Google Scholar]; Spencer, Cox-Petersen, &; Crawford, 2005 Spencer, B. H., Cox-Petersen, A. M. and Crawford, T. 2005. Assessing the impact of service-learning on preservice teachers in an after-school program. Teacher Education Quarterly, 32(4): 119–135.  [Google Scholar]). With these authentic experiences, teachers construct conceptions of literacy learning as broader than classroom teaching and learning. This study investigates how 54 preservice elementary teachers (hereafter called teachers) learned about literacy development and cultural responsivity by engaging in a service-learning experience.     

Observed Classroom Quality Profiles of Kindergarten Classrooms in Finland

Research Findings: The aim of the present study was to examine classroom quality profiles of kindergarten classrooms using a person-centered approach and to analyze these patterns in regard to teacher and classroom characteristics. Observations of the domains of Emotional Support, Classroom Organization, and Instructional Support were conducted in 49 Finnish kindergarten classrooms utilizing the Classroom Assessment Scoring System (R. C. Pianta, K. M. LaParo, &; B. K. Hamre, 2008 Pianta , R. C. , &; Hadden , D. S. ( 2008 , June ). What we know about the quality of early education settings: Implications for research on teacher preparation and professional development . The State Education Standard , pp. 20–27 . [Google Scholar]). In addition, questionnaire data on classroom and teacher characteristics, as well as Early Childhood Classroom Observation Measure (D. Stipek &; P. Byler, 2004 LaParo , K. M. , Pianta , R. C. , &; Stuhlman , M. ( 2004 ). The Classroom Assessment Scoring System: Findings from the prekindergarten year . The Elementary School Journal , 104 , 409 – 426 .[Crossref], [Web of Science ®] , [Google Scholar]) observational ratings, were used in the analyses. Latent profiling analysis was utilized to identify different profiles of classroom quality. Four latent profiles of classroom quality were identified that differed from one another most clearly in the domain of Emotional Support. Profile 1 represented a generally high level and Profile 4 a generally low level of classroom quality compared to the other profiles, whereas the medium-quality Profiles 2 and 3 showed varying levels of support in the assessed dimensions of quality. Only a few differences emerged among the profiles in classroom and teacher characteristics: The teachers in Profile 4 provided the least literacy instruction and had the least amount of work experience of all of the teachers. The findings using the Early Childhood Classroom Observation Measure indicated that child-centered practices were predominant among the profiles of higher classroom quality. Practice or Policy: The results of this study can be used to recognize kindergarten teachers' professional strengths and weaknesses and to support teachers' professional development with the aid of pedagogical interventions.     

Why Should Community College Faculty Write Grant Proposals?

Community colleges have seen dramatic enrollment increases (Kasper, 2002 Kasper , H. ( 2002 ). The changing role of community colleges . Occupational Outlook Quarterly , Winter 2002–03 , p. 19 . [Google Scholar]), and some are now offering 4-year degrees (Evelyn, 2003 Evelyn , J. ( 2003 , April 11 ). Making waves in Miami . The Chronicle of Higher Education , 49 ( 31 ), p. A34 . [Google Scholar]). They are eligible for more grants than in the past, and community college funding from state and federal appropriations is shrinking (Lawrence & Marino, 2003 Lawrence , S. & Marino , L. ( 2003 , September ). Update on funding for higher and graduate educational institutions . New York : The Foundation Center .[Crossref] , [Google Scholar]). For these reasons, it is imperative that community college faculty become involved in grant proposal preparation and submission. They will also gain professionally from participating in grant development activities.     

Evaluating Instructor Technology Integration in Community and Technical Colleges: A Performance Evaluation Matrix

The press for implementing technology based instructional delivery systems in community and technical colleges is well documented. Yet faculty face numerous challenges in integrating technology into instruction (AL-Bataineh & Brooks, 2003 AL-Bataineh , A. & Brooks , L. ( 2003 ). Challenges, advantages, and disadvantages of instructional technology in the community college classroom . Community College Journal of Research and Practice , 27 , 473 – 484 .[Taylor & Francis Online] , [Google Scholar]; Groves & Zemel, 2000 Groves , M. & Zemel , P. ( 2000 ). Instructional technology adoption in higher education: An action research case study . International Journal of Instructional Media , 27 ( 1 ), 57 – 66 . [Google Scholar]; Khoury, 1997 Khoury , R. M. ( 1997 ). The unkept promise . Community College Week , 10 ( 1 ), 4 – 6 . [Google Scholar]). Stimulating faculty ownership in technology, diffusion of technology use throughout institutions, and linking technology use to the faculty reward system are key concerns addressed in this proposed tool for evaluating faculty technology integration performance. The tool is based on research on faculty development (Howery, 1997 Howery , C. B. ( 1997 ). Recognizing and rewarding the professional and scholarly work of sociologists . Unpublished report to the Council of the American Sociological Association . [Google Scholar]) and the technology adoption process (Hall, Loucks, Rutherford, & Newlove, 1975 Hall , G. E. , Loucks , S. F. , Rutherford , W. L. , & Newlove , B. W. ( 1975 ). Levels of use of the innovation: A framework for analyzing innovation adoption . The Journal of Teacher Education , 26 ( 1 ), 52 – 56 .[Crossref], [Web of Science ®] , [Google Scholar]). Stimulating development of faculty expertise linked to technology goals is the goal of applying the tool.     

Contextualized Learning May Redefine Remedial Education

Paul Fain (2011 Fain , P. ( 2011 , September 26 ). Questioning assumptions. Inside Higher Ed. Retrieved from http://www.insidehighered.com/  [Google Scholar]), cited community college leaders who overwhelmingly voted at the Reimagining Community Colleges invitation-only conference held September 23, 2011 in New York City, for team teaching and other innovations as the most important fix for remedial education in community colleges. Team teaching is not common in postsecondary education and is difficult to do well. This paper presents the argument that it is the contextualized material that leads to team teaching success. Contextualized learning has not been rigorously researched, and it is far from having enough research for most community colleges to learn from and adapt. Although Perin (2011 Perin , D. ( 2011 ). Facilitating student learning through contextualization: A review of evidence . Community College Review , 39 ( 3 ), 268 – 295 .[Crossref] , [Google Scholar]) found that contextualized learning had been used in various ways in educational literature, this paper focuses on the integration of remedial education materials into a community college career technical skills coursework.     

Predicting Robust Learning With the Visual Form of the Moment-by-Moment Learning Curve

We present a new method for analyzing a student's learning over time for a specific skill: analysis of the graph of the student's moment-by-moment learning over time. Moment-by-moment learning is calculated using a data-mined model that assesses the probability that a student learned a skill or concept at a specific time during learning (Baker, Goldstein, & Heffernan, 2010 Baker, R. S. J. d., Goldstein, A. B. and Heffernan, N. T. 2010. “Detecting the moment of learning”. In Proceedings of the 10th Annual Conference on Intelligent Tutoring Systems 25–34. In V. Aleven, J. Kay, & J. Mostow (Eds.),pp.Heidelberg, Germany: Springer.[Crossref] , [Google Scholar], 2011). Two coders labeled data from students who used an intelligent tutoring system for college genetics. They coded in terms of 7 forms that the moment-by-moment learning curve can take. These labels are correlated to test data on the robustness of students’ learning. We find that different visual forms are correlated with very different learning outcomes. This work suggests that analysis of moment-by-moment learning curves may be able to shed light on the implications of students’ different patterns of learning over time.     

Predicting Faculty Integration of Faith and Learning

Concern regarding the secularization of Christian higher education has prompted researchers to investigate the extent that faith and learning is integrated at a faculty level and what factors might predict faculty integration (Lyon, Beaty, Parker, &; Mencken, 2005 Lyon, L., Beaty, M., Parker, J., &; Mencken, C. (2005). Faculty attitudes on integrating faith and learning at religious colleges and universities: A research note. Sociology of Religion, 66, 61–69.[Crossref], [Web of Science ®] , [Google Scholar]). This research attempted to replicate Lyon et al.’s (2005 Lyon, L., Beaty, M., Parker, J., &; Mencken, C. (2005). Faculty attitudes on integrating faith and learning at religious colleges and universities: A research note. Sociology of Religion, 66, 61–69.[Crossref], [Web of Science ®] , [Google Scholar]) logistic regression model predicting faculty integration of faith using survey responses gathered as part of Phase II of the Council for Christian Colleges &; Universities (CCCU) Denominational Study (Rine, Glanzer, &; Davignon, 2013 Davignon, P., Glanzer, P., &; Rine, P. J. (2013). Assessing the denominational identity of American evangelical colleges and universities: Part III. The student experience. Christian Higher Education, 12, 315–330. doi:10.1080/15363759.2013.825127[Taylor &; Francis Online] , [Google Scholar]). Respondents included 2,074 faculty from 55 institutions. The first model used in this study suggested that the most powerful predictors of faculty integration are full-time employment status, earning a degree from an institution that shares the same denominational affiliation, and a match between the faculty member's religious denominational affiliation and the institutional affiliation. A second logistic regression model added faculty academic specialization as a predictor of integration to investigate if that model was a better fit. Results suggested that religion and philosophy instructors are the most likely to integrate faith into their teaching, and professors specializing in computer science, math, and engineering were the least likely. As faculty are considered the primary influence on the integration of faith and learning, existing faculty and institutional administrators concerned with maintaining faith in the classroom may want to consider the contributing factors discussed.     

Influencing the College Attendance Rates of Hispanics in Texas

A number of policymakers have shifted their attention from the participation rates of Hispanics in postsecondary education to the percentage of this population that completes a baccalaureate degree. Several reports stress that while participation rates have increased, there are continued disparities in outcomes between Hispanic and White college students (President's Advisory Commission on Educational Excellence for Hispanic Americans, 2003 President's Advisory Commission on Educational Excellence for Hispanic Americans . ( 2003 ). From risk to opportunity: Fulfilling the educational needs of Hispanic Americans in the 21st Century . Washington , DC : Author . Retrieved December 14, 2006, from http://www.yic.gov/paceea/final.html  [Google Scholar]; Council of Economic Advisers, 2000 Council of Economic Advisers. (2000). Educational attainment and success in the new economy: An analysis of challenges for improving Hispanic students' achievement . Washington , DC : Author. (ERIC Document Reproduction Service No. ED442890)  [Google Scholar]; Fry, 2002 Fry , R. ( 2002 ). Latinos in higher education: Many enroll, too few graduate . Washington , DC : Pew Hispanic Center . Retrieved December 12, 2006, from http://pewhispanic.org  [Google Scholar]; Vernez & Mizell, 2001 Vernez , G. & Mizell , L. ( 2001 ). Goal: To double the rate of Hispanics earning a bachelor's degree . Santa Monica , CA : RAND . (ERIC Document Reproduction Service No. ED453771)  [Google Scholar]). Although many states have experienced increases in Hispanic postsecondary attendance, such is not the case in Texas—a state with one of the largest Hispanic populations in the country. Figures for 2003 show that 3.9% of Hispanics in Texas were enrolled in some type of postsecondary institution compared to 5.2% of African Americans and 5.6% of Caucasians (Haurwitz, 2005 Haurwitz , R. K. M. ( 2005 , January 25 ). State falling short on college enrollment: Lagging rates for Hispanics a special challenge . Austin American-Statesman . Retrieved January 2, 2007, from http://www.uh.edu/ednews/2005/aas/200501/20050125enrollment.html  [Google Scholar]).     

Self‐determined blended learning: a case study of blended learning design

Higher education has been actively encouraged to find more effective and flexible delivery models to provide all students with access to quality learning experiences yet also meet institutional imperatives for efficiency and accountability. Blended learning, commonly defined as an integration of traditional face‐to‐face and online approaches to instruction (Garrison & Kanuka, 2004 Garrison, D.R. and Kanuka, H. 2004. Blended learning: Uncovering its transformative potential in higher education. Internet and Higher Education, 7(2): 95–105.  [Google Scholar]; Graham, 2006 Graham, C.R. 2006. “Blended learning systems: Definition, current trends and future directions”. In Handbook of blended learning: Global perspectives, local designs, Edited by: Bonk, C.J. and Graham, C.R. San Francisco, CA: Pfeiffer.  [Google Scholar]; Macdonald, 2008 Macdonald, J. 2008. Blended learning and online tutoring , (2nd ed.), Hampshire, UK: Gower.  [Google Scholar]), is now proposed as one solution that addresses both student learning and higher education organisational needs. Successful blended learning, however, is more than a simple integration of information and communication technologies with face‐to‐face approaches. This paper proposes, describes and evaluates a pedagogical approach to blended learning focused on learners and learning. First, we interrogate the literature related to blended learning to show how various constructions of blended learning may be driven by teacher‐centric or learner‐centric conceptions. Next, planning a learner‐centric blended learning design for a core unit in a first year higher education course is described. The design is then evaluated using a mixed methodology in which the students’ voices illuminate their experiences of blended learning unit design with regards to engagement, learning and self‐determination.     

The Why of Learning

Alexander, Schallert, and Reynolds's (2009 Alexander, P. A., Schallert, D. L. and Reynolds, R. E. 2009. What is learning anyway? A topological perspective considered. Educational Psychologist, 44: 176–192. this issue[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]/this issue) what, where, who, and when framework situates different perspectives on learning in different places in this multidimensional space and by doing so helps us to better understand seemingly disparate approaches to learning. The framework is in need of a fifth, why dimension. The why dimension helps to place learning within an evolutionary and cultural perspective and to better understand students' motivation to learn and their preferences for what, where, and how to learn.     

Promoting Psychological Well-Being in an Urban School Using the Participatory Culture-Specific Intervention Model

School psychology has recently reconceptualized its service provision model to include multitiered systems of academic and psychosocial promotion, prevention, and intervention. The availability of evidence-based programs and advances in school consultation theory accompany the paradigm shift of the field. Despite these advances, implementing multitiered systems of support into school settings is teeming with challenges and often results in program abandonment. One often cited reason for such failures is the inattention to local priorities and culture. This article discusses the use of the participatory culture-specific intervention model (Nastasi, Moore, & Varjas, 2004 Nastasi, B. K., Moore, R. B., & Varjas, K. M. (2004). School-based mental health services: Creating comprehensive and culturally specific programs. Washington, DC: American Psychological Association.[Crossref] , [Google Scholar]) to build comprehensive systems of support in an elementary school in New Orleans. Co-authored by both researcher-consultants and school administrators, the article highlights the research, consultation, intervention, and collaborative decision-making activities over a 4-year period in a continuing university–school partnership. The discussion focuses on the process, challenges, and successes in consulting to build multitiered systems of support.     

Linear Algebra Students' Understanding of Similar Matrices and Matrix Representations of Linear Transformations in a MATLAB-Assisted Learning Environment

Abstract

The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in mathematics majors’ treatment of similar matrices and matrix representations of linear transformations in a computer-assisted learning environment by drawing primarily on three aspects of the experimental mathematics methodology, made possible by using modern digital tools to enhance learning: testing conjectures, suggesting proofs, and, computing lengthy hand derivations (Borwein &; Bailey, 2003 Borwein, J. M., &; Bailey, D. H. (2003). Experiments in mathematics: Computational paths to discovery. Natick, MA: AK Peters. [Google Scholar]). The analysis revealed a diversity of innovative ways by which research participants coordinated analytic and computational (MATLAB) methods for understanding matrix similarity and its connections to the rest of linear algebra. The paper concludes by offering pedagogical implications and recommendations for further research.     

Learning,Theories of Learning,and Units of Analysis in Research

Over the past decades research on learning has become more diverse and complex. The concern expressed by Alexander, Schallert, and Reynolds (2009 Alexander, P. A., Schallert, D. L. and Reynolds, R. E. 2009. What is learning anyway? A topographical perspective considered. Educational Psychologist, 44: 176–192. this issue[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]/this issue) is that this diversity of theoretical perspectives has resulted in a fragmentation that is destructive to the field. Although it is important to engage in explicit discussions of how learning is construed in different traditions, Alexander et al. do not give sufficient recognition to the significant epistemological and theoretical differences between traditions; differences that make them incompatible in important respects, for instance, with respect to their units of analysis. An acceptance of incompatibilities in perspectives is not necessarily a problem. In fact, such a situation may, if the debates are grounded in a mutual acceptance of the diverse manners in which knowing and learning may be theorized, give us a richer frame of reference from which to analyze learning in its various manifestations in complex societies.