Category Archives: Peer Instruction

The Non-Oppressive Mathematics Classroom: A Comprehensive Guide Towards Creating a Third Space

ETEC 521: Indigeneity, Technology, and Education

Professor: Dr. Michael Marker

December 3, 2017


Perhaps the most commonly pondered question from frustrated mathematics students, across grades and cultures, is “When am I ever going to use this?”  For exasperated fifteen-year-old Indigenous learners, this question transcends feelings of frustration; it clashes with their entire worldview. Traditionally, mathematics has been taught entirely from a Western perspective, a mindset that is firmly rooted within the pedagogy of oppression. This essay begins to address why mathematics educators need to take a step back from strictly traditional approaches, how this shift can occur within Western high school mathematics curriculum, and how Indigenous and non-Indigenous students can mathematically thrive within a culturally inclusive, third space.

Keywords:  Indigenous, non-Indigenous, mathematics, non-oppressive, worldviews, third space, high school


Protocols of Place

I would like to acknowledge that this essay was written on the traditional territory of the Lkwungen people.  I would like to further acknowledge the Songhees First Nation and the Esquimalt First Nation on whose territory I live, I learn, and I work. For the purpose of situating myself within this research essay, I am a high school mathematics and physics teacher, of White settler identity— adopted into a Norwegian family at birth, and, to my knowledge, originally from Italian and English heritage. I am primarily concerned with creating an inclusive, non-oppressive learning environment for my students, reducing the effects of anxiety in the classroom, and maintaining the academic rigor required for courses in senior mathematics and physics.


Class begins promptly at 12:20 P. M., and the agenda is on the board:

  1. Homework Questions?
  2. Hand-in homework.
  3. New section: Polynomial expansions.

Today, nobody has any questions from last night’s work.  The teacher is pleased with herself as she thinks that she must have been very effective the class before; however, this thought passes quickly, as fewer than half of her students proceed to hand in the work. She continues to teach the new lesson, as she was taught when she was in Mathematics 10.  She provides notes; students write the notes; students practice, and repeat. Her degree in mathematics has served her well—she knows what qualities the students need to succeed and to be “efficient” with their processes, as these were the qualities that she required.  If you were to ask her if she thought that she was contributing to an oppressive learning environment, she would not hesitate to say, “Absolutely not.”

The Oppressive Math Classroom

For those of us who were in high school before 2000, it is almost guaranteed that we were taught math in what is commonly called a “traditional” format, as described in the introduction. Our teachers gave notes; we wrote notes; we practiced, and were assessed. Consequently, many of us who see ourselves in the role of “math teacher” continue to teach in this traditional format. At first consideration, it may appear to be unwarranted, even outrageous, to say that learning in a traditional environment is “oppressive.”

In its most extreme form, “traditional mathematics education” can easily be equated with “math indoctrination.”  A teacher who prescribes mathematics indoctrination will provide one-sided arguments, attempt to erase learners’ differences from their processes, employ language that would pit vice against virtue, and could claim a right versus wrong way of problem-solving (Nodoushan & Pashapour, 2016).  Students in these classrooms must follow the “optimal way,” be efficient with their time, and be precise and deliberate with their strategy (Russell & Chernoff, 2012). Assessments are typically timed and performed individually, so that fully indoctrinated students will likely be successful; those who do not learn in this way risk failure, as technically this constitutes an oppressive learning environment.

In his most influential work, Pedagogy of the Oppressed, Paulo Freire describes mainstream education with the metaphor “the banking concept of education.” Although he wrote this work in 1968, it is common to find educators today possessing attitudes and following practices that imply that the teacher’s role is to merely deposit information into students as though they were receptacles. Other oppressive practices and attitudes that Freire lists include these:

  • The teacher knows everything, and the students know nothing.
  • The teacher talks, and the students listen—meekly.
  • The teacher acts and the students have the illusion of acting through the action of the teacher.
  • The teacher chooses the program content, and the students (who were not consulted) adapt to it. (p. 73, Freire)

Studies have revealed that students are less motivated in classrooms where the teacher is overly controlling, where they have fewer options for academic study, and have fewer opportunities to voice their opinions (Preston & Claypool, 2013). Should mathematics educators wish to evolve towards a non-oppressive practice, they must be prepared to loosen their academic leashes.

Also drawing from Freire’s work, Dr. Kevin Kumashiro ( has devoted his life to anti-oppressive education, amongst other forms of equalization in the classroom. Kumashiro argues that anti-oppressive teaching practices are routinely resisted when they do not fall in line with the entrenched ideations of what education is “supposed” to be.  Compacting this resistance is that, despite the good intentions of anti-oppressive sympathizers, teachers will often contribute to oppression unknowingly within their classrooms. As oppressive practices are not always identified, they may be repeated over and over, and thus experienced over and over, a cycle which results in students’ believing that there are only certain acceptable forms of identifying or thinking (Kumashiro, 2002).

On the other hand, some reformists are not simply looking at what is being done in the math classroom; rather, they are focusing on what is not being done. Stavrou and Miller maintain that, although there are many educators that recognize the disparity between Indigenous and non-Indigenous learners, there is a disconnect between what is espoused to be decolonizing, anti-oppression mathematics education and the discourse itself produced by those scholars in the field of these topics.  Often, anti-oppressive “well-meaners” will fall short in their attempts to provide decolonized education. Although they promote cultural understanding and non-Western mindsets, they neglect to address and to challenge the root causes of oppression, namely how inequalities are entrenched within our schools, and how to counter Western knowledge as superior to Indigenous ways of knowing. They also warn about the harmful effects of providing “culturally relevant mathematics” that is superficial in nature, such as teaching circular geometry by showing a medicine wheel. In circumstances where Indigenous knowledge is utilized devoid of context and meaning, not only can its use propagate stereotypes, educators risk the homogenization of Indigenous cultures and knowledge (Stavrou and Miller, 2017).  Also at risk, when simplistic versions of culturally responsive teaching are at play, is that the cultural homogenization can lead to increased instances of “othering” the non-dominant culture (Keddie, Gowlett, Mills, Monk, & Renshaw, 2012). Ultimately, practices that reinforce divisions of “us and them” are oppressive and obstructive in the creation of a safe learning environment for all. Moreover, it is critical that teachers not trivialize or decontextualize Indigenous knowledge if the learning needs of Indigenous students are to be truly valued.

Creating a Third Space

When two cultures combine and co-evolve in such a way that neither is placed as the dominant culture, but more as a new culture, some scholars describe this synthesis as representing the third space (Lipka, Sharp, Adams, & Sharp, 2007). Should there be a third space in a mathematics classroom, the new culture would have the potential to challenge existing hegemonic systems, and provide space for addressing racism and oppression, thereby creating a nurturing learning environment for all.  For the classroom to represent a third space authentically, educators must learn about the roots of oppression, such as colonization (past and present), residential schools, and racism (Stavrou & Miller, 2017).  These topics require educators to situate themselves for prolonged periods of time; considerably more time than an afternoon of Professional Development! Should teachers understand the roots of Indigenous oppression (as obvious as this will sound), non-Indigenous educators must then learn about Indigenous worldviews that can be embedded into their classroom’s third space.

Indigenous Worldviews in the Mathematics Classroom

Academic mathematics educators have many “reasons” to not embrace Indigenous worldviews within their classrooms.  These may include restrictions in teaching time, having too many learning outcomes to address, not understanding Indigenous culture or worldviews, and/or not valuing Indigenous worldviews for their subject matter.

Long before Lev Vygotsky developed his socio-cultural learning theory that focuses on the critical nature of More Knowledgeable Others (MKOs), Indigenous cultures were harnessing the wisdom of their own MKOs, namely, their elders.  Vygotskian Theory relies on MKOs to help learners flourish within their Zone of Proximal Development.  This is the space where a learner can be successful, not on their own, but with support from someone with more knowledge (John-Steiner & Mahn,1996). Elders in Indigenous communities are not only experts within their fields; they also act as conduits of culture, language, and history. Where successful examples of decolonized education have been documented, knowledge from elders is part of authentic, contextualized mathematical learning, that is far from being trivial (Lipka et al, 2007; Kawagley & Barnhardt, 1998 Preston & Claypool, 2013; Munroe, Lunney Borden, Murray Orr, Toney, & Meder, 2013).  A beautiful example of the sharing of an elder’s wisdom recently came my way on my Facebook feed. It was a video of a young girl, not more than six years old, deboning a salmon with a rather large blade.  Her mother, Margaret Neketa, was behind the camera providing encouragement, not stepping in to help physically, and allowing her daughter to make her own mistakes. At one point, the girl did make an error, and the mother calmly told her it was “okay to make mistakes”; consequently, the girl continued with even more confidence (Neketa, M., 2017). Although the little girl’s accomplishment was commendable, the magnitude of this mother’s gift of empowerment and practical, hands-on knowledge, is unmeasurable. Furthermore, how can a non-Indigenous, high school mathematics teacher draw lessons from this example of non-oppressive education?

Although academic mathematics is not traditionally “hands-on,” there are occasional opportunities that lend themselves to direct, practical experience.  Consider these examples:

  1. Surface Area: creating three-dimensional models from net diagrams.
  2. Trigonometry: using a clinometer to determine inaccessible heights.
  3. Relations and Functions: collecting actual data to graph, as opposed to using premade, tables of values.
  4. Domain and Range, Linear/Quadratic Equations, Inequalities: recreating artwork on a coordinate plane using the free, online Desmos platform (example of student work).

Although the time constraints and the number of learning outcomes to be mastered are not within an educator’s locus of control, I have found that, in my own practice, it is manageable to utilize a few practical applications within each semester. I would also reinforce the premise that to non-trivialize or decontextualize Indigenous ways of knowing, the activities should not “force” Indigeneity into the process. However, providing students with choice, such as the piece of artwork to be used in their Desmos activity, is the key because students may choose the artwork that has meaning to them.  Additionally, it is important to avoid micro-managing approaches as the students are working.  Allowing them to decide how and when they need help licenses students to have control over their learning process.  In relinquishing centralized control, educators are shifting the authority structure in their classroom, while still maintaining classroom management and the quality of the lesson content (Lipka, et al, 2007).  I do not believe that hands-on activities are possible for every lesson in academic mathematics, however, if we can occasionally weave practical applications throughout appropriate units, the result situates the learning in a non-oppressive, third space.

Collaboration with peer MKOs. Learning together via collaborative techniques is another Indigenous worldview that lends itself to mathematics in numerous ways. Vygotsky believed that MKOs could be found from all ages, not just authority figures (John-Steiner & Mahn, 1996).  In my online, ETEC 521 graduate course (Indigeneity, Technology, and Education), I watched an interview with Dr. Lee Brown, a leading expert in emotional education and creating healthy learning environments for Aboriginal learners. Here, he describes how Western culture historically promotes individualistic learning practices, whereas Indigenous cultures believe that one learns more effectively collectively.  He also maintains that, when Western classrooms fail to reflect Indigenous values, educators risk having their Indigenous students leave their classroom. What, then, can the academic mathematics teacher do both to reduce that risk and to draw from Indigenous wisdom that endorses the interconnectedness of shared knowledge?

Peer instruction. Harvard physics professor Eric Mazur is known for his alternative instructional style called peer instruction (PI).  PI is a technique in which lessons do not contain direct instruction, as the instructor’s expectation is that students will pre-read, prior to the meeting time.  Instead of direct instruction, classes include qualitative, multiple-choice questions that students vote on individually, discuss responses amongst each other, and then revote individually. The instructor moderates a class discussion that is responsive to the final voting results. Mazur explains that the success in PI is the result students’ being able to explain concepts more effectively than an experienced instructor for each other. As the peer-MKOs have only just learned the material, they have an easier time explaining from a perspective that the confused learner can more easily digest (Serious Science, 2014).

I have used a modified version of PI in my high school classroom for almost twenty years. Although I still deliver content traditionally in the form of notes, I have students discuss answers with each other throughout the lesson. Subsequently, my lessons can be noisy yet also vibrant because all students have opportunities to share their thought-processes daily. When we review material, I incorporate voting questions as directed by Mazur’s PI methodology.

Formative collaborative review. Tabletop whiteboards allow regular, small-scale review to be done collaboratively, then shown to me from across the room.  As students arrive at correct answers on their whiteboards, they become MKOs to pairs that are having difficulties.  “Snowball Math” is another technique in which students are on teams, armed with review questions that they wrote onto paper “snowballs.” For two minutes, snowballs are hurled across the room, and teams then must collaboratively solve any snowballs that were left in their zone. I just recently found this activity in a resource called the “Math First Peoples Resource Guide” (p. 22), produced by the First Nations Education Steering Committee in British Columbia. Within this guide, there is a multitude of ideas that foster third space creation.

Collaborative assessments. Mathematical assessment provides another opportunity to utilize collaborative, third space affordances. Quizzing done in a collaborative format, provides students with formative assessment, that reduces “test stress” amongst anxious mathematics learners. Allowing students the freedom to assess alone or in pairs, closed- or open-book, creates academic choice that caters to the individual needs of students. Marking their own work again shifts the responsibility towards the students, who can then obtain credit for handing in corrected work, should educators wish to record assessments.  Unit tests may also be done in a collaborative format, utilizing what is known as two-stage testing. During two-stage collaborative testing, students complete a shortened regular test individually, then in groups of four they complete the same test collaboratively.  Educators blend the two marks, say with an 80%-20% split. Students report understanding the material better, having decreased anxiety, and feeling a heightened sense of community within the class; whereas educators report higher attendance rates, lower rates of course dropouts and higher final grades (Knierim, Turner, & Davis, 2015).

As opposed to subjecting our students to repetitive forms of hegemonic oppression, these collaborative techniques repeatedly reinforce Dr. Brown’s mantra “Together, we are stronger.”  Moreover, collaborative learning practices shift the power to the students and away from the authority figure, thereby situating the learning in the third space.

Honouring multiples ways of knowing. Most high school mathematics educators have considerable experience in their field at the postsecondary level, and subsequently have an informed opinion as to how mathematical processes should optimally be done.  Optimization of process, however, is yet another practice that may be oppressive in the eyes of our students. Russell and Chernoff (2012) strike at the heart of this issue by saying, “As Indigenous students continue to struggle with mathematics teaching and learning they are concurrently struggling with yet one more aspect of this assimilation, and, thus, we are causing harm through this unethical process” (p. 116).   Traditionalists will undoubtedly take offence to the assertion that their pedagogical style is “unethical.” What is of greater concern to me, however, is that by teaching students that there is an optimal method that differs from their method, repeatedly sends the message that the students’ way of knowing is not valued. For those students who already have deep-seeded feelings of being devalued in broader contexts, rejecting their mathematical thinking may in turn perpetuate the perception that their Indigenous ways of knowing are also not valued; hence they themselves may perceive that they are not valued in our classrooms.

When multiple methodologies, in combination with cultural relevance, are presented in mathematics, students’ motivation and engagement with the mathematics increases (Kisker et al, 2011). Admittedly, in academic, high school mathematics courses, situating the mathematics within a cultural context is extremely difficult, as the mathematics is vastly learned, to perform higher levels of mathematics. Providing multiple methodologies and celebrating all forms of solutions are entirely possible in academic mathematics, however.  Expanding binomial factors, for example, can be done in a variety of ways (Table 1).

Without question, my preference is to use FOIL when expanding; however, this is of little use, should higher order polynomials be involved. Therefore, I must sometimes employ an alternative strategy. Should we require this double-barreled approach for our students as well?  In my experience, students who struggle with mathematics would prefer to learn just one strategy rather than two, so is fair to only teach to the top 50% of the class? Realistically, most students will not be taking mathematics past high school, and simply need enough academic mathematics either to graduate or possibly to enter one of countless, non-mathematics-based postsecondary programs. Moreover, it is a disservice to all our students to withhold alternative problem-solving approaches, as doing so ultimately undermines the value and creation of the third space by reinforcing a multitude of oppressive practices.

The Best of Both Worlds

Western methodologies are not without their affordances within academic mathematics contexts, and the creation of the third space allows for those affordances to remain accessible. It is also clear to me that, when educators create a third space for their students to learn within, all students benefit from this mindful effort. Helping non-Indigenous educators engage in best-practices, the case study “She Can Bother Me, and That’s Because She Cares” outlines a list of universally effective teaching strategies being used with middle school students on Baffin Island, Nunavut. Some of these strategies include the following:

  1. Adapting teaching strategies to meet the needs of the students, as opposed to having students adapt to teachers’ ways.
  2. Providing multiple learning strategies maximizes the effectiveness of students’ responses.
  3. Providing opportunities for students to voice their own strategies produces a positive learning environment.
  4. Being a caring, consistent, interested, and connected teacher who neglects student deficiencies will foster student success (Lewthwaite & McMillan, 2010).

Strict, traditional Western mathematics approaches engage in few to none of these strategies, thereby requiring Indigenous students to change, and potentially devalue, their own worldview. Sadly, this conflict of worldviews may result in the isolation of Indigenous students and their marginalization from mathematics entirely (Russell & Chernoff, 2012).

Moving forward in establishing a third space in academic mathematics classrooms, educators may follow many pathways. Providing pathways that foster resilience is a focus for some, as it is a necessary quality for students to have when developing coping strategies that mitigate stressors. York University researchers have shown that increased levels of social competency resilience and heightened appreciation of cultural identity may be fostered through Aboriginal peer mentorship programs (Rawana, Sieukaran, Nguyen, & Pitawanakwat, 2015).  In his paper entitled, “Transforming Cultural Trauma into Resilience,” Martin Brokenleg maintains that, although one can use a medicine wheel for reference, learning resilience cannot be learned from words or a poster; it must be learned through life experience. Referencing Freire’s Pedagogy of the Oppressed, Brokenleg explains that, once we are convinced that we are not good enough or smart enough, the effects of oppression are internalized and very difficult to erase from our thoughts (Brokenleg, 2012). In reality, many students entering my classes at the high school level have already internalized this harmful negativity, which I often refer to as one’s “Math Baggage.”

As a non-Indigenous educator who is mindfully making her initial steps towards the creation of a non-oppressive, third space in her mathematics classroom, I fully recognize that, in following the pedagogy described in this essay, I have merely broken the ice in considering what needs to be an ongoing journey towards a truly non-oppressive classroom.  Addressing the roots of oppression in a non-trivial way has not been addressed in this essay; nor was how to authentically embed contextualized mathematics within academic mathematics.  Nonetheless, I must follow the advice that I give to my students: a person’s not knowing how the entire solution plays out does not mean that he or she cannot at least begin to move towards a solution. Moreover, I must not be afraid to take risks and make mistakes in my learning, as I want my students to take risks and make their own mistakes in my classroom. Learning through life experience, honouring one’s identity and one’s culture, and collaboratively sharing our knowledge for the betterment of our learning community are all Indigenous worldviews that allow all students to learn at the highest levels of mathematics in a non-oppressive environment. It truly is the best of both worlds.

Brokenleg, M. (2012). Transforming cultural trauma into resilience. Reclaiming Children and Youth, 21(3), 9-13.
First Nations Education Steering Committee. (2011). Math First Peoples teacher resource guide. Retrieved from
Freire, P. (1970). Pedagogy of the oppressed. New York, NY: The Continuum International Publishing Group Inc.
John-Steiner, V., & Mahn, H. (1996). Sociocultural approaches to learning and development: A Vygotskian framework. Educational Psychologist31(3), 191. doi:10.1207/s15326985ep3103&4_4
Kawagley, A.O., & Barnhardt, R. (1998). Education Indigenous to Place: Western science meets native reality. Retrieved from
Keddie, A., Gowlett, C., Mills, M., Monk, S., & Renshaw, P. (2012). Beyond culturalism: Addressing issues of indigenous disadvantage through schooling. The Australian Educational Researcher, 40(1), 91-108. doi:10.1007/s13384-012-0080-x
Kisker, E. E., Lipka, J., Adams, B. L., Rickard, A., Andrew-Ihrke, D., Yanez, E. E., & Millard, A. (2012). The potential of a culturally based supplemental mathematics curriculum to improve the mathematics performance of Alaska Native and other students. Journal for Research in Mathematics Education, 43(1), 75.
Knierim, K., Turner, H., & Davis, R. (2015). Two-stage exams improve student learning in an introductory geology course: Logistics, attendance, and grades. Journal of Geoscience Education, 63, 157-164. Retrieved from chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/
Kumashiro, K. K. (2002). Against repetition: Addressing resistance to anti-oppressive change in the practices of learning, teaching, supervising, and researching. Harvard Educational Review, 72(1), 67.
Lipka, J., Sharp, N., Adams, B., & Sharp, F. (2007). Creating a third space for authentic biculturalism: Examples from math in a cultural context. Journal of American Indian Education, 46(3), 94-115.
Munroe, E. A., Lunney Borden, L., Murray Orr, A. Toney, D., & Meader, J. (2013). Decolonizing aboriginal education in the 21st century. McGill Journal of Education, 48(2), 317-337. doi:10.7202/1020974ar
Munroe, E. A., Lunney Borden, L., Murray Orr, A. Toney, D., & Meader, J. (2013). Decolonizing aboriginal education in the 21st century. McGill Journal of Education, 48(2), 317-337. doi:10.7202/1020974ar
Neketa, M. (2017, July 11). My one and only [Facebook post]. Retrieved from
Nodoushan, M. A. S. & Pashapour, A. (2016). Critical pedagogy, rituals of distinction, and true professionalism. I-Manager’s Journal of Educational Technology, 13(1), 20.
Preston, J. P., & Claypool, T. R. (2013). Motivators of educational success: Perceptions of Grade 12 Aboriginal students. Canadian Journal of Education. 36(4), 257-279.
Rawana, J. S., Sieukaran, D. D., Nguyen, H. T., & Pitawanakwat, R. (2015). Development and evaluation of a peer mentorship program for aboriginal university students. Canadian Journal of Education. 38(2), 1-34.
Russell, G. L., & Chernoff, E. J. (2013). The marginalisation of indigenous students within school mathematics and the math wars: Seeking resolutions within ethical spaces. Mathematics Education Research Journal, 25(1), 109-127. doi:10.1007/s13394-012-0064-1
Serious Science. (2014, June 18). Peer Instruction for Active Learning – Eric Mazur [Video file]. Retrieved from
Stavrou, S. G., & Miller, D. (2017). Miscalculations: Decolonizing and anti-oppressive discourses in indigenous mathematics education. Canadian Journal of Education, 40(3), 92-122.

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Filed under assessment, collaboration, ETEC 521, Indigenous culture, Peer Instruction, Vygotsky

An Annotated Bibliography: “Shut up and Calculate” Versus “Let’s Talk” Science Within a TELE


Teaching is an honour that I do not take for granted. Daily, I interact with close to a hundred students, within a very personal space, namely my classroom. Although, as an educator, I enact a variety of roles, primarily I serve to help students to navigate along their personal journeys in mathematics and physics. The Piagetian view that children form their knowledge via everyday life experiences opens the doors to their also fabricating presupposed models of phenomena in order to make sense of the adult world (Vosniadou & Brewer, 1992).  My goal as a teacher is to identify these “fake facts” and ideally replace what students once thought to be true, with actual truth. Admittedly, this process is easier said than done.

I do have some boys in my Science 9 class who are at a lower level, and they definitely like using Slides and being able to create that… because it is almost all boys— but they definitely enjoy using the technology a lot. As far as data, to say that it has increased their learning?  Well… they are interested in using it.

(Brown, R., personal communication, January 18, 2017)

In my own experience, the experience of my interviewee and the experience of teachers highlighted in ETEC 533’s “Grounding Issues” videos, utilizing technology within a learning environment seemingly increases student engagement, promotes collaborative working opportunities, and can produce a quality of work that implies that knowledge is being effectively transmitted. Does there exist empirical evidence, however, that can substantiate this plethora of anecdotal evidence, that technology can improve students’ understanding and resolve misunderstandings? The focus of this annotated bibliography is to discuss how teachers can address science-related student misconceptions effectively using researched methodologies in combination with effective technological practices.  I have focused on two methodologies specifically: student-generated analogies and Peer Instruction.  Peer Instruction, formally introduced by Harvard Physics professor Eric Mazur in 1997, is an interactive teaching approach that consists of introducing a problem about which students typically harbor misconceptions.  As individual students vote on their answer (with a paper ballot or other technology, such as clickers), discuss the problem amongst themselves, then revote. Class discussion then ensues, led by the instructor, but often powered by the students (Gök, 2014).

Resource Selection

Two resources were selected from UBC library collection, Summon, and one resource from the CiteULike database.  The keywords that I used for Summon were “conceptions” or “misconceptions” or “alternative conceptions” or “misunderstandings” or “challenges” or “problems” and “high school” and “students” and “technology” and “strategies” or “solutions” and “peer instruction.”  Despite my attempt to find research with high school-aged students, the papers that I found in Summon focused on post-secondary subjects, a finding which suggests that more research is being done with students whose involvement does not require parental permission and who can therefore as adults give informed consent.  I excluded articles that focused on the existence of student misconceptions, preferring articles that contained methodology that reduces or eliminates misconceptions.  In CiteULike, I found my third article simply by searching through the ETEC533’s Group Folders, specifically the folder focusing on the “Dynamics of Schooling.”  My intention was to find a study that centred on the effectiveness of technology-enhanced learning environments.

Annotated Bibliography

Haglund, J., & Jeppsson, F. (2014). Confronting conceptual challenges in thermodynamics by use of self-generated analogies. Science & Education, 23(7), 1505-1529.

The authors, researchers from the Swedish National Graduate School in Science and Technology Education, aimed to investigate the conceptual challenges that students confronted when generating analogies for complex topics, specifically in Thermodynamics, and how the students overcame these challenges. The authors defend that conceptual change occurs when a student shifts from one theory to another, referring to Vosniadou and Brewer’s framework theory (1992). Building on the Piagetian view that learning requires the accommodation of new concepts that do not quite align with pre-existing knowledge, the authors sought to examine self-generated analogies, over teacher-generated analogies, in hopes of capitalizing on socio-cultural approaches to learning. The study, involving two groups of four preservice physics teachers, required students to create as many entropy-focused analogies as possible, through situations in which students were provided “completion problems” in which entropy was partially explained, and the students were required to fill in gaps, to formulate their analogies. Scaffolding was provided to the participants’ part of the way through the process, so that students’ “idiosyncratic” notions could meet with intervention, prior to students’ creating further misconceptions. The authors identified 23 different challenges within the approximately 20 unique self-generated analogies, six of which challenges they discussed in detail. The most prevalent challenge was that the students only applied lines of microscopic reasoning to the problem, thereby routinely avoiding looking at the problem macroscopically (in terms of the First and Second Laws of Thermodynamics). The authors conclude that, although students can sometimes sort the material out on their own, teacher interventions are required to keep the students on the right path. They attribute the students’ inability to look at the problem macroscopically to the “shut-up and calculate” nature of their learning within their degree. Moreover, they conclude that student reliance on their intuition proved to be an effective vehicle not only to confront challenges in their reasoning, but to also come to terms with them.

Socio-cultural learning opportunities that address students’ learning is a practice praised by many learning theorists. It can be argued that although the authors felt that ample evidence was shown to promote using self-generated analogies, their subjects were in their fourth year of their education degrees, in the field of physics.  The external validity of their findings may not apply to high school students, who are far from specialized in the field of physics. Nonetheless, this research open the doors to replicating a similar study that focuses on high school students, which in turn may justify high school STEM teachers carving out time in their semester for more social, conversational learning, and less time with “shut-up and calculate” methodologies.

Gök, T. (2014). An investigation of students’ performance after peer instruction with stepwise problem-solving strategies. International Journal of Science and Mathematics Education, 13(3), 561-582.

A Turkish researcher from the Dokuz Eylul University, Dr. Tolga Gök, dives into analyzing a scaffolded version of Peer Instruction (PI), with two first-year university physics classes.  The quasi-experimental approach was applied to a comparison group    (n = 33, 46% female) and a treated group (n = 31, 42% female).  Both groups received PI; however, the experimental group was also instructed using stepwise problem-solving strategy (SPSS). SPSS is a strategy that breaks problems into three steps: identifying fundamental principles, solving, and checking. Gök builds his case on former studies that identify that, although students understand relevant principles and facts, they struggle with applying this information to actual problem solving. He also points out that PI has been proven not only to increase student engagement, despite students’ background knowledge, but also to reduce gender gaps in conceptual learning, and to reduce the number of students who drop the course. Gök concludes by providing ample statistics that show that SPSS with PI increased students’ physics achievement on tests and on homework assignments. He theorizes that, when students are taught how think systematically when approaching their problems, and can share this experience with their peers, they find problem-solving enjoyable and will diverge from purely “plug and chug” methodologies.


Again, this study involved university students, hence applying external validity in a high school context is not automatic.  The students in this study were relatively close in age, however, to their high school counterparts.  As ideal questions in PI have been vetted to contain common misconceptions, successfully implementing PI within a physics learning environment should theoretically work to dispel physics myths.  This research highlights the merits of SPSS implementation along with PI, something that I have never considered in my practice until now. Challenges in a high school physics class that may not exist in a university physics class would be reluctance to participate due to shyness, language barriers, or lack of confidence.  Also, with smaller class sizes, there may not be enough MKOs (more knowledgeable others) within the room, to make a positive impact on conceptual change.

Lei, J. (2010). Quantity versus quality: A new approach to examine the relationship between technology use and student outcomes. British Journal of Educational Technology, 41(3), 455-472.

The author, Dr. Jing Lei of Syracuse University, investigated quantity and quality outcomes pertaining to student outcomes. Ultimately, she reported the data from 133 of 177 students, eliminating students’ surveys which had one-third or more of the responses unanswered and those students using technology due to special needs. Citing that studies vastly differ on whether technology has increased student achievement rates, some studies, in fact, suggest that technology may even harm children.  Lei’s surveys collected information pertaining students’ demographics, technology proficiency, learning habits, and developmental outcomes (self-esteem, attitudes, social skills, etc.), and technology usage rates. To obtain information regarding academic achievement, GPAs were obtained from individual report cards. Nine students with varying interests in communication technology were selected for a single, brief interview. Her data revealed that there was no significant relationship between the quantity of technology used and student outcomes.  Technology use for socio-communication and general technological purposes had a slight increase in GPA, whereas increased entertainment/exploration and subject-specific technology uses for technology had a negative effect. The author points out, however, that none of the types of technology uses had a statistically significant effect on GPA, and that therefore educators would be wise to be realistic about the affordances that technology can provide. Lei continues by asserting that this finding does not imply that technology does not affect learning, as the categories she used were relatively broad and it was possible that factors within categories negated each other. She concludes by suggesting that research into effective uses of technology is required and that traditional methods of evaluation may not be optimal for evaluating said efficiencies.

This article did not detail the technological experience levels or training of the teachers at this school.  Without knowing this information, I am inclined to think that Lei’s results would be different were she to run the experiment in a different school. Technology’s having only a slight influence on student achievement may lead some to conclude that utilizing technology to address scientific misconceptions is not a good use of time. The categories showing slight improvements include socio-communication and general technology, however.  These categories are where science educators should potentially invest the most time in their TELE design. Moreover, how would surveys such as Lei’s be altered should educators specifically address scientific misconceptions using self-generated analogies and/or PI, assisted with technology?

Analysis of the Issue

In 1992, Vosniadou and Brewer found that 49 out of 60 children they studied held one of six models of the Earth as what they believed to be true. Only 23 of the 49 used a spherical model. These researchers conclude that, from an early age, we yearn to make sense of the world around us, basing our conclusions mostly on observations and our everyday experiences. It is thus reasonable to assume that students entering our science classes will be harbouring other presuppositions, beyond the shape of the Earth. Socio-cultural learning theory from the likes of Vygotsky and Piaget suggest that students optimally learn from interactions in their everyday surroundings and from those with whom they most frequently associate. Practices such as student-generated analogies and Peer Instruction can help educators maximize learning in a socio-cultural context by promoting “Let’s Talk” science over “Shut-up and Calculate” or “Plug and Chug” science. Although the annotated bibliography in this analysis focuses on students who are either older or younger than the high school-aged students that I teach, this merely keeps open the doors of possibility of external validity, as opposed to closing.  All three studies emphasize the importance of effective pedagogical practices. The challenge of determining what is effective, over what is not, remains to be addressed. In my experience, it is important to have students “buy in” to whatever methodology is being presented. In other words, if the students do not see value in what the exercise entails, then its effectiveness will not be actualized. Going forward, I have decided to carve specific time into my Physics classes for PI by removing designated quiz days. I will provide students with take-home quizzes with answer keys; however, during this newly acquired time slot, we will spend 80 minutes doing SPSS-PI. Using, students will be able to vote privately using their mobile devices for their ultimate answer to the question, and use table-top whiteboards to respond to the framing and checking of the question.  As I already have my Physics 11 and 12 classes authoring class blogs, I will assign each team of 3 to 4 students the task of generating and posting their analogies on the blog. Prior to posting, however, it may be important to provide scaffolding; therefore, students will initially submit their analogy on a Google Doc through which all team members can collaborate and I can provide feedback. As Lei recognized in her study, it is not the technology that makes a difference with student outcomes; rather, it is what we do with the technology that makes a difference. The scope of this analysis is limited due to not finding work that was the most up-to-date and did not use older teenagers as subjects. Further research that extends the work of Hagund, Jeppsson, Gök, and Lei to include high school students and educators who are trained in designing TELEs would be a next logical step. Should educators wish to pursue their own inquiry on a more informal approach, I have found it very useful to poll students near the end of course, to gage interest and effectiveness of whatever new methodology is being adopted. Beginning this inquiry with Eric Mazur’s book Peer Instruction: A User’s Manual is a terrific place to launch!




Brown, R. (2017, January 18). Personal interview.
Gök, T. (2014). An investigation of students’ performance after peer instruction with stepwise problem-solving strategies. International Journal of Science and Mathematics Education, 13(3), 561-582. doi:10.1007/s10763-014-9546-9
Mazur, E. (1997). Peer instruction: A user’s manual. Upper Saddle River, NJ: Prentice Hall.
Haglund, J., & Jeppsson, F. (2014). Confronting conceptual challenges in thermodynamics by use of self-generated analogies. Science & Education, 23(7), 1505-1529. doi:10.1007/s11191-013-9630-5
Lei, J. (2010). Quantity versus quality: A new approach to examine the relationship between technology use and student outcomes. British Journal of Educational Technology, 41(3), 455-472. doi:10.1111/j.1467-8535.2009.00961.x
Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24(4), 535-585. doi:10.1016/0010-0285(92)90018-W

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Filed under collaboration, ETEC 533, Misconceptions, Peer Instruction

Analysis Post: A closer look of my ETEC 533 e-Folio

Keywords from every ETEC 533 e-folio post I made:

I have always been a selfishly keen learner.

Selfish, from the perspective that I love to engage in cerebral practices that…

  1. challenge my current thinking;
  2. improve my quality of life and the quality of lives of my loved ones;
  3. keep my career choice fresh and relevant; and
  4. make me less ignorant of the issues facing society and the world, in general.

I am not entirely sure about where my lifelong quest to learn stems from, although I am certain it is not due to solely one event in my life.  Perhaps it has something to do with my parents being educators?  Perhaps I had more positive experiences in school than negative? Perhaps I am a pleaser-type— always wanting to make my teachers and parents, and now husband and children, “proud of me”? Perhaps I have a fear of appearing “stupid”?  Perhaps I just love to learn!

When looking through my e-folio posts for the course, the theme that has surfaced throughout is “student motivation”. I will further sub-categorize this theme by using the most common words from my ETEC 533 e-folio posts, shown in larger font on the above word cloud: (how we) learn and (how we) use.

Student Motivation and How We Learn

My focus early in the course was on student misconceptions. Without question, one of the most influential readings of the course was Vosniadou and Brewer’s “Mental Models of the Earth: A Study of Conceptual Change in Childhood”.  This reading, along with watching “A Private Universe”, really emphasized how students bring in their presuppositions to every learning experience and that their knowledge is situated from needing to explain the world around them (Vosniadou & Brewer, 1002). Prior to this week, I knew that students harbored misconceptions, however, not nearly to the extent that they did and why they did. Understanding that we all have an innate need to explain the world around us, whether it is scientifically based or not, has made me realize that I need to provide more opportunities within my classroom to allow students’ thinking and reasoning to be visible (Linn et al, 2002).

Throughout ETEC 533, situating and anchoring students’ learning has been a key piece that research has shown to foster students’ motivating factors.  The well-intentioned, though outdated Jasper Series week got some of us really excited to anchor learning in real life contexts.  Reading such blog posts that were titled, “Chalk and Talk are Dead” and “Goodbye Rote, Hello Anchored Instruction” exemplify this excitement to an exciting extreme. Although I will not being giving up my digital chalk anytime soon, what I have extracted from the ETEC 533 experience is that teachers of different age groups have different end goals, and hence, different pedagogical approaches, surrounding their practices.

The situated learning strategies that resonated most with me were via LfU (Learning for Use), T-GEM (Technology-enhanced: Generate, Evaluate, Modify) and embodiment. As summarized using Microsoft’s SWAY program:

All of these models naturally incorporate motivational strategies, that help engage students to want to learn.

Ultimately, students need to not only be interested in what they are learning, but they also need to have the appropriate tools in order to make that learning transpire.  Taking into account Scaffolded Knowledge Integration (SKI), in both of the activities that I have produced, incorporating the PhEt simulation for the Gravitation T-GEM and real-time data acquisition apparatus for graphical analysis, every student has an opportunity to make their learning personal and novel (Linn et al, 2002).  This concept also reinforces a key takeaway for students who were in the Spicer and Statford 2001 study analyzing the effectiveness of virtual field trips (VFT).  Students felt that by participating in the VFT, instead of a traditional lecture, that their learning had been personalized, hence they had more opportunity to engage in independent thought. With curiosity piqued (Edelson, 2000), opportunities for relationships to be generated, evaluated and modified (Khan, 2007), and interactions between the student and environment provided (Winn, 2003), self-motivation can be maximized.  In a recent post, I relayed some motivational strategies for educators to invoke:

Perhaps not if you design your practice around a few, simple motivational concepts, as outlined in the paper, “Reality versus Simulation” (Srinivasan et al, 2006):

1.       Design your lessons to “optimally challenge” your students. Like a video game, lessons shouldn’t be too difficult or too easy, for our students to engage with.

2.      Be INTERESTING. There are two key ways:

  • Weave NOVELTY into your lesson. (C+C Music Factory knows this, well.) A very smart person conducted a study that investigated K-1 students’ tendency to utilize scientific language when describing animals.  These budding, young scientists used scientific language more often when describing animals such as legless lizards and hedgehogs than when describing more common animals such as rabbits.

  • Convey a sense of IMPORTANCE and/or VALUE to what is being learned. From my own experience, ever since I began prefacing the Factoring Unit in Math 10 with, “This is the most important unit of the course” language, the unit is no longer one of the weakest units. People seem to take it more seriously when I put it on a pedestal. I also show students where I use it in my Grade 11 and 12 classes, in order to reinforce that this process is not going away any time soon.

Another key reading for myself was Winn’s “Learning in Artificial Environments: Embodiment, Embeddedness and Dynamic Adaptation” (2003).  The importance of coupling students with their environment to foster learning particularly stood out. How can we as educators capitalize on the addictive nature of video games that provide users with appropriate challenge, maximum curiosity, and opportunities to fantasize? Prior to this week, I only considered the affordances of gamification in my pedagogy.  Now, I am considering ways of using the effects of video games within my lessons.

From this post: “Activities that challenge students, pique their curiosity and provide “fruitful” new tidbits of knowledge that can assist them with future problems, are optimal, should the new knowledge wish to be adapted (Winn, 2003).”

From the same post: “As the questions would directly relate to the Vernier activity, students would be able to apply their knowledge the next day, making use of all three mechanisms for adaption of knowledge:

  1. Creating genetic algorithms: the “if-then” rules we construct when interacting with our environment and adapting our knowledge due to collecting “fruitful” information

  2. Rule Discovery: rules would have been crafted during the Vernier activity but then further entrenched by applying the rules to the Peer Instruction questions

  3. Crossover:applying the algorithms and rules in new situations could lead to rules combining into new rules for more complex situations (Winn, 2003)”

Student Motivation and How we Use

Wanting to dive into addressing student misconceptions deeper, I chose this topic as my theme for my annotated bibliography,  “Shut up and Calculate” Versus “Let’s Talk” Science Within a TELE”.   The biggest takeaway from the annotated bibliography was understanding the new roles that educators can be adopting in non-chalk-and-talk learning environments. Previously, the term “Guide on the Side” made me very uncomfortable as my interpretation of what this role entailed was limited to inquiry roles. Now, understanding the merits and dangers of using student-generated analogies (Haglund & Jeppsson, 2013) and stepwise problem-solving strategy (SPSS) (Gok, 2014), will shape my new role as “guide”.

Although I will be putting student-generated analogies and SPSS to the test in the near future, one approach that I have already adopted this semester with all three of my current classes is what I have coined as “Collaborative Quizzing”. In an attempt to create more opportunities to allow students’ thinking more visible, I now allow students to have the option of completing their quiz with a partner. This idea stemmed from our week learning about the WISE platform.  Throughout the platform, inquiry lessons require students to reflect on their learning and to provide opportunities for students to engage with each other about the topic at hand.

From this post: “Personalizing lessons within WISE, conducting class discussions, pushing students to think outside of their comfort zones and acting as the MKO (More Knowledgeable Other) at times, are all important actions and roles for educators to adopt.”

Collaborative Quizzing also came about from watching academically vulnerable students, course after course, year after year, sit through quizzes with their pencils or heads down, or with doodles of sadness strewn throughout their paper. These students will spend 20 to 30 minutes in misery, likely either negatively self-talking or in complete surrender. This is not good use of class time. As a self-described underdog, one of my goals as an educator is to help those who need the most help. So with WISE in my toolbelt and an eagerness to make class time effective, Collaborative Quizzing was born! I am particularly fascinated with the students’ feedback on the process. Overall, the feedback has been positive, and to help meet more students’ needs, I am now making the process voluntary.

As far as assessment is concerned, quizzes did not count for marks in my class, however, what I now do is require all students submit their quizzes after they have corrected their own.  I provide answer keys during the class time and upload the keys onto our Google Classroom, for those students who need more time or for those students who were away. Students receive full marks for fully corrected quizzes, as opposed to how many questions they initially got right. Increased learning interactions with peers not only build on Vygotsky theory, but also LfU theory, in that students are receiving communication directly from their MKOs to aid in the construction of knowledge (Edelson, 2000). It is theoretically possible to then immediately apply the newly constructed knowledge during the quiz and throughout the practice work that the struggling student is likely behind in.

Concluding Thoughts

Perhaps the most significant shift in my pedagogical approach to teaching math and science has been in how I utilize class time. Although five months by post-secondary standards is a very long period of time, in high school, this time is very limited.  During those five months, we teach, reinforce, provide practice time, allow for reading time, show videos, quiz, test, conduct labs, have assemblies, go on field trips, and more.  Like a bedroom closet cannot continually have pieces added to it without being dysfunctional, educators cannot continually add activities to their courses without running out of time. However, at the Grade 10 to 12 level, a reasonable expectation exists that students can and will perform some classroom responsibilities outside of class time.

With the adoption of Google Classroom, I now conduct my labs on Google Docs.  Partners can collaborate outside of class time more easily, allowing for more constructive activities to take place during class time. I have also reduced number of required practice questions with the intent of reducing the amount of in-class “worktime”, freeing up class time for more collaborative reinforcement activities.  Essentially, I am eliminating or reducing individual study activities that are in-class, in exchange for collaborative, technology-enhanced in-class activities.

Photo by Gerberkun courtesy of Imgur.

In an earlier post, I included the following image:

Motivating people to want to learn is a task that is very difficult and at times, impossible, should the approach taken be ineffective.  I do not believe that my grade levels and subject areas allow for students to pick topics that they are interested in, therefore, I need to be creative in how the material is presented and reinforced. I am very eager to take my pre-existing TELEs and make them more “T-GEM”-ized, as I did with “Conquering Mount Gravitation” and more embodied and LfU-ized, as I did with “Life on the Descoast” and “Graph Matching with Vernier”.

What is unquestionably working to my advantage in terms of motivating students to learn in my classes, is that there are not too many teachers in my school that are embracing TELEs. When students come into my class, my approaches are extremely novel and their curiosity and interest receive instant kudos—whether the lessons are effective or not. As I continue to push my personal TELE envelope, I will continue to refine and question my lessons’ effectiveness. Educators are so fortunate to have extremely user-friendly tools available to them, to make this refinement transpire. Theoretically, more educators will adopt TELEs more readily, as more of the early adopters become more fluent.

Soon, “21st Century Learners” will simply be called “Learners”– as they should be!

Edelson, D.C. (2001). Learning-for-use: A framework for the design of technology-supported inquiry activities. Journal of Research in Science Teaching,38(3), 355-385.
Gök, T. (2014). An investigation of students’ performance after peer instruction with stepwise problem-solving strategies. International Journal of Science and Mathematics
Haglund, J., & Jeppsson, F. (2014). Confronting conceptual challenges in thermodynamics by use of self-generated analogies. Science & Education, 23(7), 1505-1529. doi:10.1007/s11191-013-9630-5
Khan, S. (2007). Model-based inquiries in chemistry. Science Education, 91(6), 877-905.
Linn, M., Clark, D., & Slotta, J. (2003). Wise design for knowledge integration. Science Education, 87(4), 517-538.
Spicer, J., & Stratford, J. (2001). Student perceptions of a virtual field trip to replace a real field trip. Journal of Computer Assisted Learning, 17, 345-354.
Srinivasan, S., Perez, L. C., Palmer,R., Brooks,D., Wilson,K., & Fowler. D. (2006). Reality versus simulation. Journal of Science Education and Technology, 15(2), 137-141.
Vosniadou, S., & Brewer, W. F. (1992). Mental models of the earth: A study of conceptual change in childhood. Cognitive Psychology, 24(4), 535-585. doi:10.1016/0010-0285(92)90018-W
Winn, W. (2003). Learning in artificial environments: Embodiment, embeddedness, and dynamic adaptation. Technology, Instruction, Cognition and Learning, 1(1), 87-114.


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Filed under assessment, collaboration, Constructivism, ETEC 533, Jasper Series, Learning models, LfU, Misconceptions, Peer Instruction, Situated Learning, Vernier Probeware, Vygotsky, WISE