Introduction
Meeting My Students Where They Are
In order to drive authentic learning in a high school mathematics classroom, teachers need to scaffold learning modules that encourage members of their class to develop ‘agency’ (MacLeod, 1987) as well as the ‘strands of mathematical proficiency’ (Kilpatrick et al., 2001). The literature provides clear evidence suggesting that project-based learning (P.B.L.) and the engineering design process (E.D.P.) are two robust methodologies teachers can incorporate in an effort to drive authentic learning. This literature review summarizes how E.D.P. and P.B.L. drive mathematical fluency, flexibility, creativity and engagement in the classroom. Furthermore, I contend that E.D.P. and P.B.L. both fall under the umbrella of universal design for learning (U.D.L.)— an equitable intervention in education.
General Education is Only Geared Towards A Few Types of
Learners
In constructivist theory (Piaget, 1952) learning depends primarily upon the inner workings of the learner (i.e. not the teacher). Furthermore, “neither a knowledge base nor perceptual experience alone can be the source of cognitive development. Rather, cognitive development is the result of…interactions between the child’s thinking and reality” (Inoue, 2012, p. 78). A student approaches the world with a ‘schema’ for how he or she might tackle challenges (Inoue, 2015). Social constructivism (Vygotsky, 1978) theorizes how social and cultural inputs can either propagate or impede a learner’s cognitive development. The ‘zone of proximal development’ (Vygotsky, 1978) refers to the gap (or zone) between the ‘actual development level’ (i.e. what a child can do without assistance) and the ‘assisted development level’ (i.e. what a child can do with assistance). According to this view, “social interactions contribute to intellectual development” (Inoue, 2012, p. 96). Many students in school today are not intrinsically motivated to reach their own ‘assisted developmental level’ in mathematics. By increasing students’ social interactions, teachers can push their students further into the ‘zone of proximal development’. Accordingly, Katz (2013) expands the scope of this theory to include students with disabilities, stating that integrated classrooms report increased engagement among all students, not only those students with disabilities. I would add to this conclusion that student engagement seems to be best stimulated when the classroom incorporates learning methodologies aimed at many different types of learners. Exposing students to a variety of different ways of learning content and exploring social interaction seems to engage students, not only when their unique learning affinities are served, but throughout the curriculum arc.
Roth & Lee (2007) theorize that “persons [are] continually shaped and being shaped by their social contexts” (p. 189). Amidst this theoretical landscape, there also seems to be ample empirical research suggesting that “didactic instruction may result in short term retention of a problem solving model, but it has not been shown to lead to improved performance solving new problems” (Belland, 2011, p. 577). Furthermore, the cultivation of problem solving skills purportedly “works better in the context of instructional approaches centered on real-world problems” (Belland, 2011, p. 577). Under the premise that “humans create their cognitive powers by creating the environments in which they exercise those powers,” (Hutchins, 1995b, p. 169) it may be in the best interest of learning communities (e.g., schools) to support students by incorporating collaborative learning modules designed to engender student construction of knowledge using data collected while exploring real-world problems. By collectively defining and exploring the significance of real-world problems, students may be galvanized into action as they vet one another’s ideas and derive solutions to problems they perceive as worthy of their time and energy. To elicit this response, however, the teacher must scaffold opportunities that enlist diverse learners with myriad affinities for how information is integrated and how products of learning are conveyed. Belland’s and Hutchins’ findings suggest there is validity behind the inquiry into the effects of collecting and interpreting real data on members of an Algebra II class.
Diversity in Learners and Multiple Intelligences: Creativity & Learning, Discrimination in the Classroom, and Gardner’s Theory
Individuals are oftentimes classified as either ‘right-’ or ‘left-brained’. However, contemporary neurobiological research indicates that a person engaging in creative thought utilizes both the left and right hemispheres of the brain. Indeed, genetic affinity towards ‘right-’ or ‘left-brained’ thinking does not reign supreme as the functions within either hemisphere may be strengthened to support more robust creative thinking. According to researchers interviewed in “The Creative Brain: How Insight Works” (2015), every person has the potential to strengthen the pathways that lead to intelligent and creative thought. Moreover, a lack of creativity may indicate a sort of neglect of one or both hemispheres of the brain, in the classroom or elsewhere. This research could be interpreted to support the notion that lessons incorporating creativity are inherently more universal and therefore address the needs of diverse learners.
According to Buczynski (2015) most people are visual learners and yet most courses are catered towards verbal learners. Introducing models, E.D.P. and P.B.L. into lesson plans promotes creativity, has the capacity to serve various types of learners and can be suited to fit many different contexts. Ward, Patterson, & Sifonis (2004) claim that “avoiding readily accessible instances and accessing more abstract levels of representation reveals that people can be induced to adopt more abstract approaches in conceptual expansion tasks and that they develop more original creations as a result” (p. 99).
Within the classroom, creativity may be inadvertently stifled as teachers, challenged to provide factual knowledge to their students, overemphasize “facticity, correctness, linearity, and concreteness” (Eisner, 2002, p. 189) and in turn do little to emphasize analyzing, evaluating, imagining, and creating. Sternberg (2004) clarifies that the danger is not acquiring factual knowledge per se but emphasizing factual knowledge over the learning process.
Classroom learning is further hindered by the unconscious (and conscious) biases propagated by the teacher. According to Hehir (2002), ‘ableism’ is a discriminatory practice in which people with disabilities—cognitive, emotional and or physical— are devalued by society as they are excluded from rich experiences. This form of discrimination is also rampant in the educational sector as teachers and administrators perpetrate the ‘biomedical model perspective’ wherein “disability is viewed as a deficit, or something that needs to be remediated or cured by a team of professionals” (Morgan & Adams, 2013, p. 93). This can have a number of negative downstream implications, from feelings of isolation (Pitonyak, 2006) to increased bullying (Morgan & Adams, 2013) to decreased employment and “assumptions of deficit” (Valle & Conner, 2011, p. 61). U.D.L. suggests that while students with disabilities require and deserve different teaching strategies to address their learning, in fact all students have individual learning needs (Katz, 2013). U.D.L. supports the view that all students learn differently and should be exposed to a wide variety of learning methods (Meyer, Rose, & Gordon, 2014).
P.B.L. incorporates many cognitive tasks including expression, design, prototyping, and reflection and often promotes group work. According to Cheng et al. (2008), students assessed as both ‘high’ and ‘low’ achieving during a P.B.L. module “experienced positive group processes [and] reported a higher collective efficacy” (p. 217). This is supported by the following mean (M) and standard deviation (SD) values: ‘high’ achievers: M = + 0.12, SD = 0.47; ‘low achievers’: M = + 0.17, SD = 0.46. The data also indicates that a student’s individual efficacy is perceived as stronger during a well-scaffolded project-based lesson, especially when group efficacy is also reported to be high. Cheng et al. (2008) go on to report “a positive correlation between self- and collective efficacy (r = 0.77 and p < 0.01)” (p. 214). In other words, there is reason to believe that one’s personal efficacy is both necessary for robust group work and promoted therein.
Moreover, there is data suggesting that P.B.L., as a subset of U.D.L., creates the perception among learning communities that creativity is linked inexorably to agency. Wurdinger & Rudolph (2009) asked 147 students, teachers, parents, and alumni associated with a small charter school in Minnesota to prioritize the top three skills they learned from their school which regularly emphasizes P.B.L. Out of 371 total responses, three integral features of P.B.L.—responsibility, self-directed learning, and time management—ranked in the top three at 16%, 15%, and 13%, respectively. Additionally, when asked to define success, 94% of respondents cited ‘creativity’ as paramount. This finding converges with the research on creativity which also concludes that learning should be guided by a variety of teaching methods (Sternberg, 2004). Furthermore, Gardner’s theory of multiple intelligences (1983) suggests that learners have unique intelligence profiles with respect to verbal/linguistic, logical/mathematical, visual/spatial, musical/rhythmic, bodily/kinesthetic, interpersonal, intrapersonal, and naturalistic intelligences. Rather than a means by which to label learners, each multiple intelligence profile can be used as a baseline assessment to get to know one’s self and one’s students and craft learning modules designed to support growth areas while also catering to learners’ strengths.
Serving All Types of Learners
The classroom is an important locus for intervention insofar as it can serve as a scaffold for creative endeavors while disrupting creative bottlenecking through implementation of P.B.L. and the E.D.P. According to Moran (2010) creativity is “a novel yet appropriate solution to a problem or response to a situation” (p. 74). Moran further suggests that creativity need not be set aside for the geniuses (i.e. the few). Creativity can shift the status quo as it benefits both the individual through self expression and society through improvement. What is more, creativity can give way to wisdom if the creators themselves ruminate on the downstream implications of their creative endeavors (Helson & Srivastava, 2002). Kaufman & Sternberg (2006) and Rudowicz (2003) frame creativity as the ability to form connections, exercise cognitive flexibility, a willingness to ask questions, use imagination, experiment, value independence and self-confidence, show assertiveness, and display a high level of energy, ambition, and enthusiasm. According to Hennessey & Amabile (2010), creativity often flourishes in environments that support personal interests, champion involvement from all members, are full of enjoyment, and include challenging tasks. Given the implicit connection between creativity and meaning-making, Hennessey & Amabile’s (2010) research supports the notions that lesson plans incorporating formal critiques, multiple forms of expression, and connections to students’ personal interests could strengthen students’ perceptions of meaning.
Moran (2010) suggests that creative processes and products are influenced by multiple parties and that “society’s impact can be passed among three roles: benefactor, regulator, and consumer” (p. 78). In this model, the benefactors impact the early stages of creativity as they “provide resources enabling creativity” while the regulators act as the “bottleneck of creativity” insofar as they select “which ideas and products are worthy of support, development, and dissemination” (p. 78). Since classmates can provide feedback (i.e. intellectual resources) they may be positioned to serve as ‘benefactors’ of creative endeavors within schools. The teacher may serve as a ‘regulator’ who influences how the creative process develops and how the creative product is shared with others: the ‘consumers’ (e.g., members of the class, the school, and larger community). P.B.L. and the E.D.P. tend to shake up the roles that students and teacher habitually fall into. As such, they are useful teaching tools for shifting the status quo and breaking up the ‘creativity bottleneck’.
Fluency and Flexibility Through Project-Based Learning and the Engineering Design Process
In her presentation entitled “The How: Developing a Creative Environment in the S.T.E.M. Classroom”, Hansen (2015) asserts that P.B.L. emphasizes the ‘four C’s’: creativity, collaboration, communication, and critical thinking. It would seem that these tenets of P.B.L., when paired with appropriate scaffolding and encouragement from the teacher, should help students gain fluency (i.e. the ability to generate many ideas) and flexibility (i.e. the ability to examine a problem from a second or third vantage point) through opportunities that cultivate original, meaningful works. P.B.L. seems to provide one setting for students to unleash and sharpen their creative potential. Ertmer (2014) outlines five principles of rigorous P.B.L.: real-world connections, core to learning, structural collaboration, student-driven, and multifaceted in assessment. Similarly, E.D.P. promotes learning in science and mathematics classrooms insofar as it affords students the opportunity to address their preconceptions, organize factual and conceptual knowledge into a cogent network, engage metacognitively, and develop the five strands of mathematical proficiency (Kilpatrick et al., 2001).
In longitudinal studies from 1932 to 2010, Rinne et al. (2011) found learners remember novel information that they generate better than if they had simply read that information. P.B.L. and the E.D.P. can serve as a conduit for students realizing the application for otherwise-abstract studies. Furthermore, technological devices—used, prototyped or conceived of--may “determine the possible trajectories of information or the kinds of transformations of information structure that are required for propagation” (Hutchins, 1995b, p. 287) while opening the door for formal critiques, multiple forms of expression, and connections to students’ personal interests. There is also the capacity for classroom units rooted in P.B.L. and the E.D.P to incorporate art making and, in turn, heighten creativity since “in art making, learners not only apply information, they apply it imaginatively” (Buczinski , 2015). As subsets of U.D.L., the E.D.P. and P.B.L. can be viewed as logical tools to encourage increased agency and equitable access to learning amongst diverse learners.
Universal Design for Learning as an Equitable Intervention
U.D.L. represents a mitigation of ableist practices and added scaffolding for all types of learners (i.e. not only the disability-labeled). U.D.L. helps meet the needs of diverse learners and provides multiple means of engagement, representation, action and expression (Rose & Meyer, 2012). Features of U.D.L. include equitable use and access for all students, flexibility in accommodations, cogency of instruction, ease of use of materials, and information that is “successful[ly] communicat[ed] to the student” through multi-sensory tools (Valle & Conner, 2011, p. 78). U.D.L. also calls for formative assessments and valuing relationship-based education modeled by an enthusiastic, compassionate teacher who celebrates diversity, holds high standards for all, and guides students through frequent feedback and assessments so “all learners [have] a fair chance to show what they feel, know, and can do” (Meyer, Rose & Gordon, 2014, p. 75).
Classrooms are becoming increasingly diverse vis-à-vis racial background and disability (Thousand, Villa, & Nevin, 2007). Per their multiple intelligence profiles, students gravitate towards a variety of sensory experiences. U.D.L. imbues a wide array of methodologies that serve these diverse preferences for learning while satisfying legal mandates by offering “better instruction, equality of opportunity to learn, and excellence in performance for all children” (Thousand, Villa & Nevin, 2007, p. 4). This equality of opportunity extends to the entire educational experience—not just the curricular. U.D.L. caters to a holistic view of education by valuing content, processes and products of learning. During a study of behavior at ten K-12 schools, Katz (2013) measured
engagement using a one-minute time sampling procedure of control and variable student groups before and after implementing a sixty-minute U.D.L. workshop. The data indicates an increase in mean engagement from 41.54 to 54.52 minutes in the variable group (N = 56; SD = 10.23) and a decrease in engagement from 50.18 to 43.64 minutes in the control group (N = 44; SD = 7.98). There was a difference in engagement when juxtaposing the variable and control groups. Given that P.B.L. and the E.D.P. encourage students creatively to make meaningful works, then creativity, P.B.L., and the E.D.P. should be considered paramount in the classroom. By encouraging students to embrace iterative, creative products teachers can push their students into custodianship of knowledge thereby amplifying and exercising their agency. I hypothesize that my research project will build on the connection between agency and the tenets of a U.D.L. curriculum arc within a high school Algebra II class. Robinson (2006) proclaims, “creativity is as important as literacy and we should treat it with the same respect.” If P.B.L. and E.D.P. modules are creativity-driven and made relevant, they can inspire ‘catalytic validity’ (Inoue, 2015) by empowering, focusing, and galvanizing students. This research project presupposes that some of the effects of a U.D.L. classroom that makes use of P.B.L. and the E.D.P. will demonstrate said catalytic validity with students being empowered, focused, and galvanized.
Implicitly, U.D.L. and social constructivism (Vygotsky, 1978) are highly compatible through ethical implementation of democratic values (e.g., culturally responsive instruction, preparing informed citizens who can resolve conflict, share responsibility and respect diversity). Moreover, both U.D.L. and social constructivism challenge all students to take on leadership roles that make use of personal talents and interests while having their learning needs met in an inclusive, student-centered classroom. Increased student and teacher efficacy, agency, and sense of belonging are also central consequences of differentiated instruction within the U.D.L classroom.
Conclusion
The body of research on agency and U.D.L. suggests that all students learn differently—not only those who are disabled—and students are better served when teachers draw on methodologies that address all types of learners equally. It follows that a classroom that employs a variety of teaching methods will stimulate students not only when the particular student’s learning proficiency is touched upon, but also when the student is exposed to an inclusive scope and breadth of teaching methods that stimulate new pathways of learning. Furthermore, the intermingling of individual and group learning modules is an effective way to invite students to venture into their ‘zone of proximal development’. The literature indicates that E.D.P. and P.B.L. could be interpreted as tools to deploy during a U.D.L. curriculum arc since they support diverse learners and, through a variety of methodologies, promote student agency. U.D.L. represents an equitable intervention in the classroom that attempts to ensure that each student is given the same opportunity to develop his or her agency, which in turn leads to increased student engagement and creativity. It seems evident from the literature that an inquiry into the effects of U.D.L. on members of an Algebra II course could result in valuable data regarding student agency, creative explorations of real-world problems, cognitive fluency & flexibility, and strands of mathematical proficiency.
References
Artful thinking: Stronger thinking and learning through the power of art. (2006).
Retrieved July 5, 2016, from http://pzartfulthinking.org/wp-content/uploads/2014/09/ArtfulThinkingFinalReport-1.pdf
BBC Documentary -- The creative brain: How insight works. (2015, July 17). Retrieved
June 1, 2016, from http://www.dailymotion.com/video/x1gn21d_bbc-documentary-horizon-the-creative-brain-how-insight-works_lifestyle
Belland, B. R. (2011). Distributed cognition as a lens to understand the effects of
scaffolds: The role of transfer of responsibility. Educational Psychology Review Educ Psychol Rev, 23(4), 577-600. Retrieved June 4, 2016, from http://0-web.b.ebscohost.com.sally.sandiego.edu/ehost/pdfviewer/pdfviewer?vid=24&sid=8f480ef1-ca98-4cae-8d65-b190dc4273fa@sessionmgr114&hid=115
Berland, L., Steingut, R., & Ko, P. (2014). High school student perceptions of the utility
of the engineering design process: Creating opportunities to engage in engineering practices and apply math and science content. Journal of Science Education and Technology, 23(6), 705-720. doi:10.1007/s10956-014-9498-4
Buczynski, S. (2015). The art of learning and art strategies. Lecture presented at the
University of San Diego, San Diego.
Cheng, R. W.-yi, Lam, S.-fong, & Chan, J. C.-yan. (2008). When high achievers and low
achievers work in the same group: the roles of group heterogeneity and processes in project-based learning. The British Journal of Educational Psychology, 78(2), 205-221. doi: 10.1348/000709907X218160.
Eisner, E. W. (2002). The arts and the creation of mind. New Haven, CT: Yale
University Press
Engineering design process video series. (2014). Retrieved June 9, 2015, from
http://www.nasa.gov/audience/foreducators/best/index.html
Ertmer, P. (2014, June 25). Five keys to rigorous project-based learning. Retrieved
May 29, 2016, from http://www.edutopia.org/video/five-keys-rigorous-project-based-learning
Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York:
Basic Books.
Hansen, B. (Lecturer) (2015, January 1). The how: Developing a creative environment
in the STEM classroom. Lecture conducted from University of San Diego, San Diego.
Hehir, T. (2002). Eliminating ableism in education. Harvard Educational Review, 72(1),
1-33. Retrieved March 7, 2016, from https://ole.sandiego.edu/bbcswebdav/pid-761309-dt-content-rid-1442815_1/courses/EDUC-X538-MASTER/M1/M1_EliminatingAbleism.pdf.
Helson, R., & Srivastava, S. (2002). Creative and wise people: Similarities, differences,
and how they develop. Personality and Social Psychology Bulletin, 28, 1430-1440.
Hennessey, B. A., & Amabile, T. M. (2010). Creativity. Annual Review of Psychology,
61, 569–598.
Hutchins, E. (1995b). Cognition in the wild. Cambridge, MA: MIT Press.
Inoue, N. (2015). Beyond actions: Psychology of action research for mindful educational
improvement. Educational Psychology.
Inoue, N. (Lecturer) (2015, September). Lecture 2.2: The brain. Lecture presented in
University of San Diego, San Diego.
Inoue, N. (Lecturer) (2015, September). Lecture 3.1:Piaget’s theory of cognitive
development. Lecture presented at University of San Diego, San Diego.
Inoue, N. (2012). Mirrors of the mind: Introduction to mindful ways of thinking
education. New York, New York: Peter Lang.
Katz, J. (2013). Implementing the three block model of universal design for learning:
Effects on teachers' self-efficacy, stress, and job satisfaction in inclusive classrooms K-12. Canadian Journal of Education, 36(1), 153-194. doi:10.1080/13603116.2014.881569
Kaufman, J. C., & Sternberg, R. J. (2006). Resource review: Creativity. Change, 39, 55–
58
Kilpatrick, J. , Swafford, J. , & Findell, B. (2001). Adding it up: Helping children learn
mathematics. Washington, DC: National Academy Press.
MacLeod, J. (1987). Ain’t no making it. Leveled aspirations in a low income
neighborhood. Westview Press: Colorado.
Meyer, A., Rose, D.H., & Gordon, D. (2014). Designing for all: What is a UDL
curriculum. In Universal design for learning: Theory and practice (pp. 68-84). Wakefield, MA: CAST
Moll, L., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for
teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 132-141.
Moran, S. (2010). The roles of creativity in society. In The Cambridge Handbook of
Creativity. Cambridge: Cambridge University Press.
Morgan, J., & Adams, D. (2013). Bullying and students with disabilities: The bully, the
bullied, and the misunderstood. In Miller, S., Burns, L., & Johnson, T.S. (Authors), Generation BULLIED 2.0: Prevention and intervention strategies for our most vulnerable students (pp. 87-112). New York, NY: Peter Lang.
National council of teachers of mathematics (2000). NCTM principles and standards
for school mathematics electronic version. Reston, VA
Piaget, J. (1952). The origins of intelligence in children. New York: International
Universities Press.
Pitonyak, D. (2006). The importance of belonging. TASH Connections, 32(1), 1-3.
Retrieved April 20, 2016, from http://www.dimagine.com/TASHbelonging.pdf
Rinne, L., Gregory, M., Yarmolinskyay, J., and Hardiman, M. (2011). Why arts
integration improves long-term retention of content. Mind, Brain, and Education. 5(2): 89-96.
Robinson, K. (July 2006). Do schools kill creativity? TED Conferences. New York, NY.
Retrieved from http://www.ted.com/talks/ken_robinson_says_schools_kill_creativity
Rose, A., & Meyer, D.H. (2012). The three principles of universal design for learning.
Retrieved June 2, 2016, from http://www.udlcenter.org/aboutudl/whatisudl/3principles
Roth, W., & Lee, Y. (2007). Vygotsky's neglected legacy: Cultural-historical activity
theory. Review of Educational Research, 77(2), 186-232. Retrieved May 24, 2016, from http://eva.universidad.edu.uy/pluginfile.php/354845/mod_resource/content/0/S6_LA3_Roth_Lee_VygotskyCHAT_2007.pdf
Rudowicz, E. (2003). Creativity and culture: A two way interaction. Scandinavian
Journal of Educational Research, 47(3), 273.
Sternberg, R. J. (2004). Four alternative futures for education in the United States. It’s
our choice. School Psychology Review, 33, 67-77.
Thousand, J. S., Villa, R. A., & Nevin, A. (2007). Differentiating instruction:
Collaborative planning and teaching for universally designed learning. Thousand Oaks, CA: Corwin Press.
Valle, J. W., & Conner, D. J. (2011). Rethinking disability: A disability studies approach
to inclusive practices. New York, NY: McGraw-Hill.
Vygotsky, L.S. (1978). Mind in society: The development of higher psychological
processes. Cambridge, MA: Harvard University Press.
Ward, T., Patterson, M., & Sifonis, C. (2004). The Role of specificity and abstraction in
creative idea generation. Creativity Research Journal, 16(1), 1-99. doi:2004
Wurdinger, S., & Rudolph, J. (2009). A different type of success: Teaching important life
skills through project-based learning. Improving Schools, 12(2), 115-129.
Meeting My Students Where They Are
In order to drive authentic learning in a high school mathematics classroom, teachers need to scaffold learning modules that encourage members of their class to develop ‘agency’ (MacLeod, 1987) as well as the ‘strands of mathematical proficiency’ (Kilpatrick et al., 2001). The literature provides clear evidence suggesting that project-based learning (P.B.L.) and the engineering design process (E.D.P.) are two robust methodologies teachers can incorporate in an effort to drive authentic learning. This literature review summarizes how E.D.P. and P.B.L. drive mathematical fluency, flexibility, creativity and engagement in the classroom. Furthermore, I contend that E.D.P. and P.B.L. both fall under the umbrella of universal design for learning (U.D.L.)— an equitable intervention in education.
General Education is Only Geared Towards A Few Types of
Learners
In constructivist theory (Piaget, 1952) learning depends primarily upon the inner workings of the learner (i.e. not the teacher). Furthermore, “neither a knowledge base nor perceptual experience alone can be the source of cognitive development. Rather, cognitive development is the result of…interactions between the child’s thinking and reality” (Inoue, 2012, p. 78). A student approaches the world with a ‘schema’ for how he or she might tackle challenges (Inoue, 2015). Social constructivism (Vygotsky, 1978) theorizes how social and cultural inputs can either propagate or impede a learner’s cognitive development. The ‘zone of proximal development’ (Vygotsky, 1978) refers to the gap (or zone) between the ‘actual development level’ (i.e. what a child can do without assistance) and the ‘assisted development level’ (i.e. what a child can do with assistance). According to this view, “social interactions contribute to intellectual development” (Inoue, 2012, p. 96). Many students in school today are not intrinsically motivated to reach their own ‘assisted developmental level’ in mathematics. By increasing students’ social interactions, teachers can push their students further into the ‘zone of proximal development’. Accordingly, Katz (2013) expands the scope of this theory to include students with disabilities, stating that integrated classrooms report increased engagement among all students, not only those students with disabilities. I would add to this conclusion that student engagement seems to be best stimulated when the classroom incorporates learning methodologies aimed at many different types of learners. Exposing students to a variety of different ways of learning content and exploring social interaction seems to engage students, not only when their unique learning affinities are served, but throughout the curriculum arc.
Roth & Lee (2007) theorize that “persons [are] continually shaped and being shaped by their social contexts” (p. 189). Amidst this theoretical landscape, there also seems to be ample empirical research suggesting that “didactic instruction may result in short term retention of a problem solving model, but it has not been shown to lead to improved performance solving new problems” (Belland, 2011, p. 577). Furthermore, the cultivation of problem solving skills purportedly “works better in the context of instructional approaches centered on real-world problems” (Belland, 2011, p. 577). Under the premise that “humans create their cognitive powers by creating the environments in which they exercise those powers,” (Hutchins, 1995b, p. 169) it may be in the best interest of learning communities (e.g., schools) to support students by incorporating collaborative learning modules designed to engender student construction of knowledge using data collected while exploring real-world problems. By collectively defining and exploring the significance of real-world problems, students may be galvanized into action as they vet one another’s ideas and derive solutions to problems they perceive as worthy of their time and energy. To elicit this response, however, the teacher must scaffold opportunities that enlist diverse learners with myriad affinities for how information is integrated and how products of learning are conveyed. Belland’s and Hutchins’ findings suggest there is validity behind the inquiry into the effects of collecting and interpreting real data on members of an Algebra II class.
Diversity in Learners and Multiple Intelligences: Creativity & Learning, Discrimination in the Classroom, and Gardner’s Theory
Individuals are oftentimes classified as either ‘right-’ or ‘left-brained’. However, contemporary neurobiological research indicates that a person engaging in creative thought utilizes both the left and right hemispheres of the brain. Indeed, genetic affinity towards ‘right-’ or ‘left-brained’ thinking does not reign supreme as the functions within either hemisphere may be strengthened to support more robust creative thinking. According to researchers interviewed in “The Creative Brain: How Insight Works” (2015), every person has the potential to strengthen the pathways that lead to intelligent and creative thought. Moreover, a lack of creativity may indicate a sort of neglect of one or both hemispheres of the brain, in the classroom or elsewhere. This research could be interpreted to support the notion that lessons incorporating creativity are inherently more universal and therefore address the needs of diverse learners.
According to Buczynski (2015) most people are visual learners and yet most courses are catered towards verbal learners. Introducing models, E.D.P. and P.B.L. into lesson plans promotes creativity, has the capacity to serve various types of learners and can be suited to fit many different contexts. Ward, Patterson, & Sifonis (2004) claim that “avoiding readily accessible instances and accessing more abstract levels of representation reveals that people can be induced to adopt more abstract approaches in conceptual expansion tasks and that they develop more original creations as a result” (p. 99).
Within the classroom, creativity may be inadvertently stifled as teachers, challenged to provide factual knowledge to their students, overemphasize “facticity, correctness, linearity, and concreteness” (Eisner, 2002, p. 189) and in turn do little to emphasize analyzing, evaluating, imagining, and creating. Sternberg (2004) clarifies that the danger is not acquiring factual knowledge per se but emphasizing factual knowledge over the learning process.
Classroom learning is further hindered by the unconscious (and conscious) biases propagated by the teacher. According to Hehir (2002), ‘ableism’ is a discriminatory practice in which people with disabilities—cognitive, emotional and or physical— are devalued by society as they are excluded from rich experiences. This form of discrimination is also rampant in the educational sector as teachers and administrators perpetrate the ‘biomedical model perspective’ wherein “disability is viewed as a deficit, or something that needs to be remediated or cured by a team of professionals” (Morgan & Adams, 2013, p. 93). This can have a number of negative downstream implications, from feelings of isolation (Pitonyak, 2006) to increased bullying (Morgan & Adams, 2013) to decreased employment and “assumptions of deficit” (Valle & Conner, 2011, p. 61). U.D.L. suggests that while students with disabilities require and deserve different teaching strategies to address their learning, in fact all students have individual learning needs (Katz, 2013). U.D.L. supports the view that all students learn differently and should be exposed to a wide variety of learning methods (Meyer, Rose, & Gordon, 2014).
P.B.L. incorporates many cognitive tasks including expression, design, prototyping, and reflection and often promotes group work. According to Cheng et al. (2008), students assessed as both ‘high’ and ‘low’ achieving during a P.B.L. module “experienced positive group processes [and] reported a higher collective efficacy” (p. 217). This is supported by the following mean (M) and standard deviation (SD) values: ‘high’ achievers: M = + 0.12, SD = 0.47; ‘low achievers’: M = + 0.17, SD = 0.46. The data also indicates that a student’s individual efficacy is perceived as stronger during a well-scaffolded project-based lesson, especially when group efficacy is also reported to be high. Cheng et al. (2008) go on to report “a positive correlation between self- and collective efficacy (r = 0.77 and p < 0.01)” (p. 214). In other words, there is reason to believe that one’s personal efficacy is both necessary for robust group work and promoted therein.
Moreover, there is data suggesting that P.B.L., as a subset of U.D.L., creates the perception among learning communities that creativity is linked inexorably to agency. Wurdinger & Rudolph (2009) asked 147 students, teachers, parents, and alumni associated with a small charter school in Minnesota to prioritize the top three skills they learned from their school which regularly emphasizes P.B.L. Out of 371 total responses, three integral features of P.B.L.—responsibility, self-directed learning, and time management—ranked in the top three at 16%, 15%, and 13%, respectively. Additionally, when asked to define success, 94% of respondents cited ‘creativity’ as paramount. This finding converges with the research on creativity which also concludes that learning should be guided by a variety of teaching methods (Sternberg, 2004). Furthermore, Gardner’s theory of multiple intelligences (1983) suggests that learners have unique intelligence profiles with respect to verbal/linguistic, logical/mathematical, visual/spatial, musical/rhythmic, bodily/kinesthetic, interpersonal, intrapersonal, and naturalistic intelligences. Rather than a means by which to label learners, each multiple intelligence profile can be used as a baseline assessment to get to know one’s self and one’s students and craft learning modules designed to support growth areas while also catering to learners’ strengths.
Serving All Types of Learners
The classroom is an important locus for intervention insofar as it can serve as a scaffold for creative endeavors while disrupting creative bottlenecking through implementation of P.B.L. and the E.D.P. According to Moran (2010) creativity is “a novel yet appropriate solution to a problem or response to a situation” (p. 74). Moran further suggests that creativity need not be set aside for the geniuses (i.e. the few). Creativity can shift the status quo as it benefits both the individual through self expression and society through improvement. What is more, creativity can give way to wisdom if the creators themselves ruminate on the downstream implications of their creative endeavors (Helson & Srivastava, 2002). Kaufman & Sternberg (2006) and Rudowicz (2003) frame creativity as the ability to form connections, exercise cognitive flexibility, a willingness to ask questions, use imagination, experiment, value independence and self-confidence, show assertiveness, and display a high level of energy, ambition, and enthusiasm. According to Hennessey & Amabile (2010), creativity often flourishes in environments that support personal interests, champion involvement from all members, are full of enjoyment, and include challenging tasks. Given the implicit connection between creativity and meaning-making, Hennessey & Amabile’s (2010) research supports the notions that lesson plans incorporating formal critiques, multiple forms of expression, and connections to students’ personal interests could strengthen students’ perceptions of meaning.
Moran (2010) suggests that creative processes and products are influenced by multiple parties and that “society’s impact can be passed among three roles: benefactor, regulator, and consumer” (p. 78). In this model, the benefactors impact the early stages of creativity as they “provide resources enabling creativity” while the regulators act as the “bottleneck of creativity” insofar as they select “which ideas and products are worthy of support, development, and dissemination” (p. 78). Since classmates can provide feedback (i.e. intellectual resources) they may be positioned to serve as ‘benefactors’ of creative endeavors within schools. The teacher may serve as a ‘regulator’ who influences how the creative process develops and how the creative product is shared with others: the ‘consumers’ (e.g., members of the class, the school, and larger community). P.B.L. and the E.D.P. tend to shake up the roles that students and teacher habitually fall into. As such, they are useful teaching tools for shifting the status quo and breaking up the ‘creativity bottleneck’.
Fluency and Flexibility Through Project-Based Learning and the Engineering Design Process
In her presentation entitled “The How: Developing a Creative Environment in the S.T.E.M. Classroom”, Hansen (2015) asserts that P.B.L. emphasizes the ‘four C’s’: creativity, collaboration, communication, and critical thinking. It would seem that these tenets of P.B.L., when paired with appropriate scaffolding and encouragement from the teacher, should help students gain fluency (i.e. the ability to generate many ideas) and flexibility (i.e. the ability to examine a problem from a second or third vantage point) through opportunities that cultivate original, meaningful works. P.B.L. seems to provide one setting for students to unleash and sharpen their creative potential. Ertmer (2014) outlines five principles of rigorous P.B.L.: real-world connections, core to learning, structural collaboration, student-driven, and multifaceted in assessment. Similarly, E.D.P. promotes learning in science and mathematics classrooms insofar as it affords students the opportunity to address their preconceptions, organize factual and conceptual knowledge into a cogent network, engage metacognitively, and develop the five strands of mathematical proficiency (Kilpatrick et al., 2001).
In longitudinal studies from 1932 to 2010, Rinne et al. (2011) found learners remember novel information that they generate better than if they had simply read that information. P.B.L. and the E.D.P. can serve as a conduit for students realizing the application for otherwise-abstract studies. Furthermore, technological devices—used, prototyped or conceived of--may “determine the possible trajectories of information or the kinds of transformations of information structure that are required for propagation” (Hutchins, 1995b, p. 287) while opening the door for formal critiques, multiple forms of expression, and connections to students’ personal interests. There is also the capacity for classroom units rooted in P.B.L. and the E.D.P to incorporate art making and, in turn, heighten creativity since “in art making, learners not only apply information, they apply it imaginatively” (Buczinski , 2015). As subsets of U.D.L., the E.D.P. and P.B.L. can be viewed as logical tools to encourage increased agency and equitable access to learning amongst diverse learners.
Universal Design for Learning as an Equitable Intervention
U.D.L. represents a mitigation of ableist practices and added scaffolding for all types of learners (i.e. not only the disability-labeled). U.D.L. helps meet the needs of diverse learners and provides multiple means of engagement, representation, action and expression (Rose & Meyer, 2012). Features of U.D.L. include equitable use and access for all students, flexibility in accommodations, cogency of instruction, ease of use of materials, and information that is “successful[ly] communicat[ed] to the student” through multi-sensory tools (Valle & Conner, 2011, p. 78). U.D.L. also calls for formative assessments and valuing relationship-based education modeled by an enthusiastic, compassionate teacher who celebrates diversity, holds high standards for all, and guides students through frequent feedback and assessments so “all learners [have] a fair chance to show what they feel, know, and can do” (Meyer, Rose & Gordon, 2014, p. 75).
Classrooms are becoming increasingly diverse vis-à-vis racial background and disability (Thousand, Villa, & Nevin, 2007). Per their multiple intelligence profiles, students gravitate towards a variety of sensory experiences. U.D.L. imbues a wide array of methodologies that serve these diverse preferences for learning while satisfying legal mandates by offering “better instruction, equality of opportunity to learn, and excellence in performance for all children” (Thousand, Villa & Nevin, 2007, p. 4). This equality of opportunity extends to the entire educational experience—not just the curricular. U.D.L. caters to a holistic view of education by valuing content, processes and products of learning. During a study of behavior at ten K-12 schools, Katz (2013) measured
engagement using a one-minute time sampling procedure of control and variable student groups before and after implementing a sixty-minute U.D.L. workshop. The data indicates an increase in mean engagement from 41.54 to 54.52 minutes in the variable group (N = 56; SD = 10.23) and a decrease in engagement from 50.18 to 43.64 minutes in the control group (N = 44; SD = 7.98). There was a difference in engagement when juxtaposing the variable and control groups. Given that P.B.L. and the E.D.P. encourage students creatively to make meaningful works, then creativity, P.B.L., and the E.D.P. should be considered paramount in the classroom. By encouraging students to embrace iterative, creative products teachers can push their students into custodianship of knowledge thereby amplifying and exercising their agency. I hypothesize that my research project will build on the connection between agency and the tenets of a U.D.L. curriculum arc within a high school Algebra II class. Robinson (2006) proclaims, “creativity is as important as literacy and we should treat it with the same respect.” If P.B.L. and E.D.P. modules are creativity-driven and made relevant, they can inspire ‘catalytic validity’ (Inoue, 2015) by empowering, focusing, and galvanizing students. This research project presupposes that some of the effects of a U.D.L. classroom that makes use of P.B.L. and the E.D.P. will demonstrate said catalytic validity with students being empowered, focused, and galvanized.
Implicitly, U.D.L. and social constructivism (Vygotsky, 1978) are highly compatible through ethical implementation of democratic values (e.g., culturally responsive instruction, preparing informed citizens who can resolve conflict, share responsibility and respect diversity). Moreover, both U.D.L. and social constructivism challenge all students to take on leadership roles that make use of personal talents and interests while having their learning needs met in an inclusive, student-centered classroom. Increased student and teacher efficacy, agency, and sense of belonging are also central consequences of differentiated instruction within the U.D.L classroom.
Conclusion
The body of research on agency and U.D.L. suggests that all students learn differently—not only those who are disabled—and students are better served when teachers draw on methodologies that address all types of learners equally. It follows that a classroom that employs a variety of teaching methods will stimulate students not only when the particular student’s learning proficiency is touched upon, but also when the student is exposed to an inclusive scope and breadth of teaching methods that stimulate new pathways of learning. Furthermore, the intermingling of individual and group learning modules is an effective way to invite students to venture into their ‘zone of proximal development’. The literature indicates that E.D.P. and P.B.L. could be interpreted as tools to deploy during a U.D.L. curriculum arc since they support diverse learners and, through a variety of methodologies, promote student agency. U.D.L. represents an equitable intervention in the classroom that attempts to ensure that each student is given the same opportunity to develop his or her agency, which in turn leads to increased student engagement and creativity. It seems evident from the literature that an inquiry into the effects of U.D.L. on members of an Algebra II course could result in valuable data regarding student agency, creative explorations of real-world problems, cognitive fluency & flexibility, and strands of mathematical proficiency.
References
Artful thinking: Stronger thinking and learning through the power of art. (2006).
Retrieved July 5, 2016, from http://pzartfulthinking.org/wp-content/uploads/2014/09/ArtfulThinkingFinalReport-1.pdf
BBC Documentary -- The creative brain: How insight works. (2015, July 17). Retrieved
June 1, 2016, from http://www.dailymotion.com/video/x1gn21d_bbc-documentary-horizon-the-creative-brain-how-insight-works_lifestyle
Belland, B. R. (2011). Distributed cognition as a lens to understand the effects of
scaffolds: The role of transfer of responsibility. Educational Psychology Review Educ Psychol Rev, 23(4), 577-600. Retrieved June 4, 2016, from http://0-web.b.ebscohost.com.sally.sandiego.edu/ehost/pdfviewer/pdfviewer?vid=24&sid=8f480ef1-ca98-4cae-8d65-b190dc4273fa@sessionmgr114&hid=115
Berland, L., Steingut, R., & Ko, P. (2014). High school student perceptions of the utility
of the engineering design process: Creating opportunities to engage in engineering practices and apply math and science content. Journal of Science Education and Technology, 23(6), 705-720. doi:10.1007/s10956-014-9498-4
Buczynski, S. (2015). The art of learning and art strategies. Lecture presented at the
University of San Diego, San Diego.
Cheng, R. W.-yi, Lam, S.-fong, & Chan, J. C.-yan. (2008). When high achievers and low
achievers work in the same group: the roles of group heterogeneity and processes in project-based learning. The British Journal of Educational Psychology, 78(2), 205-221. doi: 10.1348/000709907X218160.
Eisner, E. W. (2002). The arts and the creation of mind. New Haven, CT: Yale
University Press
Engineering design process video series. (2014). Retrieved June 9, 2015, from
http://www.nasa.gov/audience/foreducators/best/index.html
Ertmer, P. (2014, June 25). Five keys to rigorous project-based learning. Retrieved
May 29, 2016, from http://www.edutopia.org/video/five-keys-rigorous-project-based-learning
Gardner, H. (1983). Frames of mind: The theory of multiple intelligences. New York:
Basic Books.
Hansen, B. (Lecturer) (2015, January 1). The how: Developing a creative environment
in the STEM classroom. Lecture conducted from University of San Diego, San Diego.
Hehir, T. (2002). Eliminating ableism in education. Harvard Educational Review, 72(1),
1-33. Retrieved March 7, 2016, from https://ole.sandiego.edu/bbcswebdav/pid-761309-dt-content-rid-1442815_1/courses/EDUC-X538-MASTER/M1/M1_EliminatingAbleism.pdf.
Helson, R., & Srivastava, S. (2002). Creative and wise people: Similarities, differences,
and how they develop. Personality and Social Psychology Bulletin, 28, 1430-1440.
Hennessey, B. A., & Amabile, T. M. (2010). Creativity. Annual Review of Psychology,
61, 569–598.
Hutchins, E. (1995b). Cognition in the wild. Cambridge, MA: MIT Press.
Inoue, N. (2015). Beyond actions: Psychology of action research for mindful educational
improvement. Educational Psychology.
Inoue, N. (Lecturer) (2015, September). Lecture 2.2: The brain. Lecture presented in
University of San Diego, San Diego.
Inoue, N. (Lecturer) (2015, September). Lecture 3.1:Piaget’s theory of cognitive
development. Lecture presented at University of San Diego, San Diego.
Inoue, N. (2012). Mirrors of the mind: Introduction to mindful ways of thinking
education. New York, New York: Peter Lang.
Katz, J. (2013). Implementing the three block model of universal design for learning:
Effects on teachers' self-efficacy, stress, and job satisfaction in inclusive classrooms K-12. Canadian Journal of Education, 36(1), 153-194. doi:10.1080/13603116.2014.881569
Kaufman, J. C., & Sternberg, R. J. (2006). Resource review: Creativity. Change, 39, 55–
58
Kilpatrick, J. , Swafford, J. , & Findell, B. (2001). Adding it up: Helping children learn
mathematics. Washington, DC: National Academy Press.
MacLeod, J. (1987). Ain’t no making it. Leveled aspirations in a low income
neighborhood. Westview Press: Colorado.
Meyer, A., Rose, D.H., & Gordon, D. (2014). Designing for all: What is a UDL
curriculum. In Universal design for learning: Theory and practice (pp. 68-84). Wakefield, MA: CAST
Moll, L., Amanti, C., Neff, D., & Gonzalez, N. (1992). Funds of knowledge for
teaching: Using a qualitative approach to connect homes and classrooms. Theory Into Practice, 132-141.
Moran, S. (2010). The roles of creativity in society. In The Cambridge Handbook of
Creativity. Cambridge: Cambridge University Press.
Morgan, J., & Adams, D. (2013). Bullying and students with disabilities: The bully, the
bullied, and the misunderstood. In Miller, S., Burns, L., & Johnson, T.S. (Authors), Generation BULLIED 2.0: Prevention and intervention strategies for our most vulnerable students (pp. 87-112). New York, NY: Peter Lang.
National council of teachers of mathematics (2000). NCTM principles and standards
for school mathematics electronic version. Reston, VA
Piaget, J. (1952). The origins of intelligence in children. New York: International
Universities Press.
Pitonyak, D. (2006). The importance of belonging. TASH Connections, 32(1), 1-3.
Retrieved April 20, 2016, from http://www.dimagine.com/TASHbelonging.pdf
Rinne, L., Gregory, M., Yarmolinskyay, J., and Hardiman, M. (2011). Why arts
integration improves long-term retention of content. Mind, Brain, and Education. 5(2): 89-96.
Robinson, K. (July 2006). Do schools kill creativity? TED Conferences. New York, NY.
Retrieved from http://www.ted.com/talks/ken_robinson_says_schools_kill_creativity
Rose, A., & Meyer, D.H. (2012). The three principles of universal design for learning.
Retrieved June 2, 2016, from http://www.udlcenter.org/aboutudl/whatisudl/3principles
Roth, W., & Lee, Y. (2007). Vygotsky's neglected legacy: Cultural-historical activity
theory. Review of Educational Research, 77(2), 186-232. Retrieved May 24, 2016, from http://eva.universidad.edu.uy/pluginfile.php/354845/mod_resource/content/0/S6_LA3_Roth_Lee_VygotskyCHAT_2007.pdf
Rudowicz, E. (2003). Creativity and culture: A two way interaction. Scandinavian
Journal of Educational Research, 47(3), 273.
Sternberg, R. J. (2004). Four alternative futures for education in the United States. It’s
our choice. School Psychology Review, 33, 67-77.
Thousand, J. S., Villa, R. A., & Nevin, A. (2007). Differentiating instruction:
Collaborative planning and teaching for universally designed learning. Thousand Oaks, CA: Corwin Press.
Valle, J. W., & Conner, D. J. (2011). Rethinking disability: A disability studies approach
to inclusive practices. New York, NY: McGraw-Hill.
Vygotsky, L.S. (1978). Mind in society: The development of higher psychological
processes. Cambridge, MA: Harvard University Press.
Ward, T., Patterson, M., & Sifonis, C. (2004). The Role of specificity and abstraction in
creative idea generation. Creativity Research Journal, 16(1), 1-99. doi:2004
Wurdinger, S., & Rudolph, J. (2009). A different type of success: Teaching important life
skills through project-based learning. Improving Schools, 12(2), 115-129.