Amber Davidson Theory Review

Environment and Context in Relation to Mathematical Learning

Amber Davidson

EDAC 635: Strategies for Teaching Adults

Theory Review

Dr. Bo Chang

September 24, 2021

 

Name	Commented On: Group # (Date)
Amber Davidson	Amanda Sabo: Group 1 (09/28/2021)
	Alicia Denton: Group 2 (10/03/2021)

 

Main Theoretical Points

     Most people naturally gravitate to working or studying in an environment that feels comfortable.  Some prefer settings like the library where there are very little distracting environmental stimuli.  Others prefer to work in a café, park, or other setting where there are more auditory, visual, and sensory stimuli.  According to Immes and Kvan (2021), “instinctively, we all care about the spaces in which we conduct our daily lives” (p. 3) and the decisions we make about our learning environment have some influence on our performance.  

     Klee, Miller, and Buehl (2021) reports that “up to 30% of adults report moderate or severe mathematics anxiety (Dowker et al., 2016), experiencing fear or dread when encountering mathematics (Richardson & Suinn, 1972)” (p. 1).  Environmental factors influence student’s motivation which, in turn, influence their anxiety, learning, and performance.  As facilitators we need to “learn to think critically about our learning environments and the contexts before they become problematic” (MacKeracher, 2004, p. 187).  Each student comes to class with differing needs, preferences, and beliefs and there are five aspects of the learning environment that affect every student.      

 

Physical Environment

            The physical learning environment refers to all physical properties of the place where teaching and learning take place (Choi, van Merrienboer, & Paas, 2014).  According to MacKeracher (2004) the physical environment also refers to “anything affecting the physical comfort and well-being of both learners and facilitators” (p. 187).  The physical aspects of the environment can be categorized into either the ergonomics or the technology that is present.  The ergonomics of the physical environment include the comfort of the seating, sound quality and level, light and visual quality, and the air quality.  Each of these can affect learners either in a positive way or have a distracting and negative affect on the learner.  The technology in the classroom may also have a distracting effect on learning if not used properly. 

            If there are too many physical distractions within the environment, these factors may “influence individuals’ motivational factors which influence mathematics anxiety and subsequent performance” (Klee et al., 2021, p. 2).  For example, based on studies the air quality and “thermal conditions of a learning environment can affect an individual’s learning performance through oxygen-related physiological mechanisms” (Choi et al., 2014, p. 232).  When the quality of the physical learning environment is poor, students emotional state may be influenced which will ultimately negatively impact learning by reducing “learners’ willingness to allocate cognitive resources to the learning task” (p. 234).  

            It is the facilitators responsibility to manipulate and make good use of the tools within the physical learning space.  According to Choi, van Merrienboer, and Paas (2014), since the stimuli from the physical learning environment can impose a load on learners’ working memory, it needs to be utilized to “manage learners’ cognitive load and so improve learning” (p. 244).  Immes and Kvan (2021) suggest as facilitators, when we see an opportunity in a room, we use it and when the “physical space no longer suffices, we adapt, we workaround, we hack” (p. 5).  Thus, the physical environmental factors and their effect on the cognitive load, can be “regarded as a determinant of the effectiveness of instruction” (Choi et al., 2014, p. 225).  

            

Cultural Environment

            MacKeracher (2004) states the culture of a learning environment is the “system of learned beliefs, values, assumptions, customs, language, meanings, and behaviors shared” (p. 192) between the facilitator and students.  Learning is influenced by culture since it provides “tools, habits, and assumptions that pervasively influence human thought and behavior” (Tweed & Lehman, 2002, p. 89).  There are many problems associated with the invisible assumptions that accompany different cultural beliefs.  When we encounter different cultures, the differences may be unknown, and the uncertainty may increase our stress and anxiety.  “When we do not understand the cultural differences between ourselves and others ‘offense can be unwittingly given or taken’ (Noble, 2000, p.9)” (MacKeracher, 2004, p. 194).   Students themselves are constantly developing who they are and who they want to become which affects students “participation and engagement in school and mathematics” (Lester, 2007, p. 409).  

        According to Muis (2004) it is the facilitators role to mediate between “students’ meanings and the culturally established mathematical meanings of the larger society” (p. 322).  The teacher is a part of the learning environment and therefore “can affect students’ anxiety, cognitive load, and learning” (Choi et al., 2014, p. 234).  For example, in a study completed by Jackson and Leffingwell (1999), students reported boys were helped more than girls, girls were often ridiculed for not understanding, and when girls asked questions, some teachers laughed at them.  Girls that endorse the stereotype that boys are better at math and girls are better at reading, “showed less math learning across the school year” (Choi et al., 2014, p. 234).  When the female teacher showed anxiousness about math, the girls in the class were more likely to agree with this stereotype.  It is imperative that instructors make themselves “aware of their impact on students” (Jackson & Leffingwell, 1999, p. 585).  

        Lester (2007) found there are many “discontinuities between students’ ways of reasoning, talking, and interacting rooted in their out-of-school communities and those of their mathematics classroom” (p. 408).  Classroom and activity structures that encourage open participation and that “afford negotiation around the framing and positioning of participation, are more likely to encourage broad-based participation among a range of students” (p. 409).  The field of mathematics “perpetuates a culture that excludes individuals with different perspectives (such as minorities and women)” and “progress on equity cannot be made…as long as deficit perspectives continue to permeate research and practice” (p. 415).  Students’ academic roles and behaviors are culturally influenced but “students and educators alike may under appreciate such influences affecting and given student” (Tweed & Lehman, 2002).  Educators must become inter-culturally competent, be aware of our own culture and how it influences others, acknowledge and encourage diversity, and confront inequities that arise in the classroom environment (MacKeracher, 2004).  

 

Power Environment

            “The differences between cultures are also accompanied by power imbalances” (MacKeracher, 2004, p. 194).  We can understand social power as a “feature of all social interactions that operates on both macro (structural) and micro (interactional) levels.  Power both constructs and is reinforced through the hierarchies within which individuals interact” (Vanstone & Grierson, 2020, p. 182).  Vanstone and Grierson also point out the features of the environment influence motivation, and people interact with those features to support their own learning.  According to MacKeracher (2004), the interactions among individuals in the learning environment “create a learning context in which power, its sources and uses, become crucial elements” (p. 196).  

        Power is typically seen as something that is enacted by higher-status individuals toward lower-status individuals as determined by the specific social environment. However, lower-status individuals can influence the nature of the interactions in how they respond to demonstrations of power (Vanstone & Grierson, 2020).  When students are given the opportunity to have more control over their situation, “they tend to exhibit lower anxiety” (Khlee et al., 2021, p. 3).  Jackson and Leffingwell (1999) discuss the role instructors have on students’ math anxiety.  In order to reduce student’s anxiety, it is essential to make “mutual respect a pervasive rule to ensure that the classroom environment is psychologically safe” (p. 586).  

        Facilitators must “provide an environment in which learners can find their voice in a supportive and safe atmosphere (Tisdell, 2000)” (MacKeracher, 2004, p. 196).  By identifying and analyzing how power influences the policies, structure, and individuals within the environment, facilitators can “work to attenuate the harm perpetuated by those sources” (Vanstone & Grierson, 2020, p. 182-83).  Facilitators must also recognize, analyze, confront, and call attention to power-related incidents that occur within the learning environment (MacKeracher, 2004).           

 

Knowledge Environment

            “Knowledge is the basis for acting in and upon the world: ‘Knowledge enables us to perceive, act, and move in a world, and as we act, perceive, and move the world comes forth as a result of our actions and observations’ (von Krogh and Roos, 1995, p. 51)” (Miller & Lin, 2010).  Muis (2004) defines epistemology as “a branch of philosophy concerned with the nature of knowledge and justification of belief” (p. 317).  MacKeracher (2004) states there is possibly one epistemology for every human and each person’s personal model of reality is just as much an epistemology as another’s.  The development of epistemological beliefs are influenced by changes and experiences, including educational experiences, in one’s life and are thus revised throughout life (Muis, 2004).  According to Muis (2004), in the context of mathematics, epistemological beliefs include perspectives on the nature, justifications, sources and “acquisition of mathematics knowledge” (p. 326).

        Muis (2004) discusses how individuals have an unconscious system of beliefs that effect how they comprehend, solve problems, and react to challenging tasks.  These beliefs are “likely to affect reasoning, learning, and decision making and to have both direct and indirect effects on learning” (p. 320).  Many students believe mathematical knowledge is unchanging, that it is passively handed down by instructors, and that only those with an “innate ability” can learn math on their own (p. 330).  It has been found that the more students believe that knowledge is inert or have this “simple knowledge” perspective, the worse they did on comprehension tests (p. 342).   Muis also explains how “formal mathematics education plays a major role in the development of students’ beliefs about the nature of mathematical knowledge” (p. 339).  Choi and Hannafin (1995) state many formal math learning experiences are decontextualized and the learning of facts “are isolated from the contexts in which they derive meaning” and when mathematics instruction is presented as decontextualized and simplified knowledge, it “promotes understanding that is rigid, incomplete, and naïve” (p. 53).             

 

Real-Life Environment

            According to Choi and Hannafin (1995), “it appears that both knowledge and cognitive skills are highly dependent on the contexts in which they are acquired” (p. 57).  Many students find it difficult to apply the knowledge and skills they have acquired in formal learning to every day contexts.   MacKeracher (2004) defines the term ‘situated cognition’ as “an emerging body of ideas covering both the nature of learning and the design of learning experiences” (p. 201). Choi and Hannafin (1995) extend the definition to include that situated cognition also provides meaningful learning that promotes the “transfer of knowledge to real-life situations” (p. 53).   

            In a situated learning environment, the goal is for students to “process information deeply and restructure knowledge accordingly, and to apply knowledge and skills flexibly across related problems” (Choi & Hannafin, 1995, p. 64).  MacKeracher (2004) states “all knowledge is contextually situated and is fundamentally influenced by the activity, context, and culture in which it is developed and used (Brown, Collins, & Duguid, 1989)” (p. 201).  The context provides the framework for learning and the situated learning environment “provide a broader, more inclusive way to conceptualize the process” (Choi & Hannafin, 1995, p. 67).  

            Since most formal learning settings, especially in mathematics, emphasize symbolic and decontextualized knowledge, facilitators need to incorporate more real-life experiences in informal learning contexts.  In doing this, students can apply knowledge practically to solve “everyday problems” (Choi & Hannafin, 1995, p. 54).  Choi and Hannafin (1995) discuss how many times instructors try to include context in instruction, but the problems still promote “uniform rather than unique understanding” (p. 56).  When instruction is rooted in problem-based contexts, “students acquire knowledge as well as a sense of when and how to use it” (p. 60).  In a situated learning environment, real-life experiences are valued, and students learn “during experience, rather that merely from experience (Jacobson, 1996)” (MacKeracher, 2004, p. 203).    

 

Application

            There are certain characteristics of the physical environment that students prefer when learning or working on tasks.  It is the responsibility of the facilitator to carefully plan and manipulate the physical learning space to help make the students comfortable.  Negative effects of physical environment factors should “always be minimized or, if possible, eliminated” (Choi et al., 2014).  For example, this may include altering the seating arrangement in the classroom to meet the instructional goals, fixing a buzzing light, adjusting the lighting so everyone can see properly at different points during the session, and making sure all classroom technology is working properly so there are no interruptions (MacKeracher, 2004).  The use of “esthetically appealing design in multimedia learning materials” may lead to students having more positive emotions and make the learning tasks seem less difficult (Choi et al., 2014, p. 234).  

            MacKeracher (2004) states “culture is never neutral. It pervades the teaching-learning environment, brought there by both learners and facilitator” (p. 193).  As facilitators we need to become inter-culturally competent, learn to communicate effectively, actively listen, avoid projecting our own model of reality onto others, and allow others to be who they are.  We need to be aware of the power relationships and interactions between the students and be “critically aware of how our own positionality affects our behavior” (p. 197).  Jackson and Leffingwell (1999) acknowledge that instructor behavior is an important factor that can cause math anxiety and instructors need to “provide an environment, through positive attitudes and sound pedagogy, that is conductive to students’ success as mathematics learners” (p. 586).  Facilitators can also learn more about their students’ individual and diverse needs and discuss any cultural or power related conflicts that may arise. 

            “Meaning is not universal but is influenced heavily by cultural factors: ‘The community and its viewpoint determine how [knowledge] is used (p. 33)” (Choi & Hannafin, 1995, p. 58).  An example Choi and Hannafin (1995) give is how carpenters and cabinet makers use chisels differently and how mathematics is used differently by physicists and mathematicians.  It is important for us, as facilitators, to know how the knowledge and tools we give students will function within their culture, meet their needs, and reflect the real-life context that is relevant to them.  Differing epistemological beliefs may also cause conflicts and facilitators need to address these conflicts and listen carefully to better understand the diverse student population (MacKeracher, 2004).  

            Facilitators can use situated cognition to promote connections between knowledge, skill, and experience through context-based learning experiences (Choi & Hannafin, 1995).  MacKeracher (2004) lists many types of context-based learning experiences like telling stories, reflection-in-action, apprenticeships, collaborative activities, providing coaching and mentorships, situational learning, and simulations.  The knowledge and skills needed for adult activities and skills “can be learned most effectively within the actual contexts where they are used” (p. 202).  

 

Reflection

            Before learning about this topic, I only thought of the physical and emotional aspects of the learning environment.  I wanted to make sure students were comfortable, could see the board, and could hear everything during class.  I also wanted them to feel comfortable in my classroom on an emotional level, but I had not thought too much about what that looked like specifically.  

            After learning about the five different aspects of the learning environment, I can now more easily determine what I specifically need to do in order to create a positive environment for my students.  For example, in addition to the physical features of the room I also need to make sure my facilitation reflects the type of environment suitable for learning for all my students’ diverse needs.  By giving my students more open-ended tasks I can help them feel more empowered in my classroom.  By giving students more opportunities to collaborate, I can help students gain more of a sense of community with each other.  I need to make sure I acknowledge my culture, epistemology, and how my position affects my students.  I need to make sure I learn more about my students’ individual needs and concerns so I can do a better job of creating a safe space for all my students.  

Last, I need to make sure I use more situated learning experiences in my class.  As a math teacher, I have lots of improvement to be done in this area.  My students need more real-life context in order to make the content and knowledge they acquire more valuable and usable in the real-world.  By making the content related to different cultures, contexts, and life experiences, I create a better and more meaningful learning environment for my students.    

  

Highlights

            A highlight of this assignment has been the additional experience with research I have gained.  Another highlight has been how much more I have learned about how important it is for me to acknowledge and analyze the diversity within my classes.  I have never truly acknowledged how much influence I have on students learning outside of content knowledge.  The effect my actions, words, and presence have on students is more significant than I had realized.  I am now more aware of my role as a facilitator and how I affect the learning environment.  

 

Process

            After reading the MacKeracher (2004) chapter on Environment and Context I read through the discussions on the Canvas discussion board for Unit 4.  Reading through the summaries of the five different aspects of the learning environment that other students write helped me gain a better understanding of them.  began searching for articles on the Ball State Library website.  I then searched for articles related to math learning environments, math anxiety, and the five aspects of the learning environment.  I saved the articles I found and printed most of them out so I could write notes on them.  As I read through each one I labeled the different parts of the article I found the most important by underlining or writing in the margins.  After creating a detailed outline of each section, I wrote my paper.

 

Table 1. Summary of Theoretical Ideas

	The main theoretical ideas	Summary of how to apply the main theoretical ideas in practice
Idea 1	Physical Environment:  Physical discomfort can inhibit student learning.	Physical environmental distractions should either be minimized or eliminated because these factors can influence student’s motivation, anxiety, learning, and performance. It is the facilitators responsibility to manipulate and make good use of the tools within the physical learning space.
Idea 2	Cultural Environment:  The different cultures brought by students and the facilitator influence thought, behavior, and learning.	Classroom and activity structures that encourage open participation are more likely to encourage participation among a wide range of students. As facilitators we need to become inter-culturally competent, learn to communicate effectively, actively listen, avoid projecting our own model of reality onto others, and allow others to be who they are.
Idea 3	Power Environment: Facilitators need to be aware of how their positionality affects student learning.	Facilitators must provide an environment in which learners can find their voice in a supportive and safe atmosphere. We need to be aware of the power relationships and interactions between the students, be aware of how our own positionality affects our behavior, and address and power-related instances that occur in the classroom.
Idea 4	Knowledge Environment:  Each students’ epistemology and model of reality should be acknowledged and valued.	Differing epistemological beliefs may cause conflicts and facilitators need to address these conflicts and listen carefully to better understand the diverse student population. Mathematics instruction needs to be presented through context-based experiences to avoid incomplete and inapplicable knowledge.
Idea 5	Real-Life Environment:  Knowledge is contextually situated and context-based experiences make learning relevant.	Facilitators need to incorporate more real-life experiences in informal learning contexts.  In doing this, students can apply knowledge practically to solve real-life problems.

 

 References

Choi, H.-H., van Merriënboer, J. J., & Paas, F. (2014). Effects of the physical environment on cognitive load and learning: Towards a new model of cognitive load. Educational Psychology Review, 26(2), 225–244. https://doi.org/10.1007/s10648-014-9262-6 

Choi, J.-I., & Hannafin, M. (1995). Situated Cognition and learning environments: Roles, structures, and implications for design. Educational Technology Research and Development, 43(2), 53–69. https://doi.org/10.1007/bf02300472 

Imms, W., & Kvan, T. (2021). Teacher transition into Innovative Learning Environments: A global perspective. Springer. 

Jackson, C. D., & Leffingwell, R. J. (1999). The role of instructors in creating math anxiety in students from kindergarten through college. The Mathematics Teacher, 92(7), 583–586. https://doi.org/10.5951/mt.92.7.0583 

Klee, H. L., Miller, A. D., & Buehl, M. M. (2021). Strategies for alleviating students’ math anxiety: Control-value theory in practice. Theory Into Practice. https://doi.org/10.1080/00405841.2021.1932157 

Lester, F. K. (2007). Second Handbook of Research on Mathematics Teaching and learning. Information Age.

MacKeracher, D. (2004). Making sense of adult learning. University of Toronto Press. 

Miller, K. D., & Lin, S.-J. (2010). Different truths in different worlds. Organization Science, 21(1), 97–114. https://doi.org/10.1287/orsc.1080.0409 

Muis, K. R. (2004). Personal epistemology and mathematics: A critical review and synthesis of Research. Review of Educational Research, 74(3), 317–377. https://doi.org/10.3102/00346543074003317 

Tweed, R. G., & Lehman, D. R. (2002). Learning considered within a cultural context: Confucian and Socratic approaches. American Psychologist, 57(2), 89–99. https://doi.org/10.1037/0003-066x.57.2.89 

Vanstone, M., & Grierson, L. (2020). Social power facilitates and constrains motivation in the Clinical Learning Environment. Medical Education, 54(3), 181–183. https://doi.org/10.1111/medu.14046